Magma V2.20-8     Mon Oct  6 2014 23:09:45 on mathcompprd01 [Seed = 3934839593]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/eobr007/.magma.startup"

> 
> n := 12;
> p := 2;
> G := Sym (n);
> RandomSchreier (G);
> order := #G;
> Dims := [[44, 100]];
> Primes := [2];
> dims := Dims[1];
> p := 2;
>  I := IrreducibleModules (G, GF (p): MaxDegree := Maximum (dims));
>  J := [x : x in I | Dimension (x) in dims];
> L := [ActionGroup (j): j in J];
> O := [LMGOrder (l): l in L];
> L := [L[i]: i in [1..#L] | O[i] eq #G];
> "Faithful reps over GF(", p, ") have dimensions:", [Degree (l): l in L], "\n";
Faithful reps over GF( 2 ) have dimensions: [ 44, 100 ]


> 
> f,phi, tau := RecogniseAlternatingOrSymmetric (L[1]);
> H:=sub<G | (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11), (1,2)>; 
> CompositionFactors (H);
    G
    |  Cyclic(2)
    *
    |  Alternating(11)
    1
> S := sub<Generic (L[1]) | [tau (H.i): i in [1..2]]>;
> IsIrreducible (S);
true
> 
> f,phi, tau := RecogniseAlternatingOrSymmetric (L[2]);
> S := sub<Generic (L[2]) | [tau (H.i): i in [1..2]]>;
> IsIrreducible (S);
true
> 
> n := 14;
> p := 2;
> G := Sym (n);
> RandomSchreier (G);
> order := #G;
> Dims := [[208]];
> Primes := [2];
> dims := Dims[1];
> p := 2;
>  I := IrreducibleModules (G, GF (p): MaxDegree := Maximum (dims));
 *** ERROR -- not all irreducible modules found.
>  J := [x : x in I | Dimension (x) in dims];
> L := [ActionGroup (j): j in J];
> O := [LMGOrder (l): l in L];
> L := [L[i]: i in [1..#L] | O[i] eq #G];
> "Faithful reps over GF(", p, ") have dimensions:", [Degree (l): l in L], "\n";
Faithful reps over GF( 2 ) have dimensions: [ 208 ]


> 
> f,phi, tau := RecogniseAlternatingOrSymmetric (L[1]);
> H:=sub<G | (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13), (1,2)>; 
> CompositionFactors (H);
    G
    |  Cyclic(2)
    *
    |  Alternating(13)
    1
> S := sub<Generic (L[1]) | [tau (H.i): i in [1..2]]>;
> IsIrreducible (S);
true
> 
> n := 16;
> p := 2;
> G := Sym (n);
> RandomSchreier (G);
> order := #G;
> Dims := [[128]];
> Primes := [2];
> dims := Dims[1];
> p := 2;
>  I := IrreducibleModules (G, GF (p): MaxDegree := Maximum (dims));
 *** ERROR -- not all irreducible modules found.
>  J := [x : x in I | Dimension (x) in dims];
> L := [ActionGroup (j): j in J];
> O := [LMGOrder (l): l in L];
> L := [L[i]: i in [1..#L] | O[i] eq #G];
> "Faithful reps over GF(", p, ") have dimensions:", [Degree (l): l in L], "\n";
Faithful reps over GF( 2 ) have dimensions: [ 128 ]


> 
> f,phi, tau := RecogniseAlternatingOrSymmetric (L[1]);
> H:=sub<G | (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15), (1,2)>; 
> CompositionFactors (H);
    G
    |  Cyclic(2)
    *
    |  Alternating(15)
    1
> S := sub<Generic (L[1]) | [tau (H.i): i in [1..2]]>;
> IsIrreducible (S);
true
> 
> SetEchoInput (false);
Loading "s18-d256-f2"
Loading "z.m"
> 
> L := [G];
> n := 18;
> p := 2;
> G := Sym (n);
> RandomSchreier (G);
> order := #G;
> "Faithful reps over GF(", p, ") have dimensions:", [Degree (l): l in L], "\n";
Faithful reps over GF( 2 ) have dimensions: [ 256 ]


> 
> f,phi, tau := RecogniseAlternatingOrSymmetric (L[1]);
> H:=sub<G | (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17), 
(1,2)>; 
> CompositionFactors (H);
    G
    |  Cyclic(2)
    *
    |  Alternating(17)
    1
> S := sub<Generic (L[1]) | [tau (H.i): i in [1..2]]>;
> IsIrreducible (S);
true
> 
> SetEchoInput (false);
Loading "s20-d512-f2"
Loading "z.m"
> L := [G];
> 
> n := 20;
> p := 2;
> G := Sym (n);
> RandomSchreier (G);
> order := #G;
> "Faithful reps over GF(", p, ") have dimensions:", [Degree (l): l in L], "\n";
Faithful reps over GF( 2 ) have dimensions: [ 512 ]


> 
> f,phi, tau := RecogniseAlternatingOrSymmetric (L[1]);
> H:=sub<G | (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 
19), (1,2)>; 
> CompositionFactors (H);
    G
    |  Cyclic(2)
    *
    |  Alternating(19)
    1
> S := sub<Generic (L[1]) | [tau (H.i): i in [1..2]]>;
> IsIrreducible (S);
true

Total time: 5154.319 seconds, Total memory usage: 9391.69MB