Magma V2.20-10 Sun Mar 1 2015 16:18:24 on mathcompprd01 [Seed = 3631881280] Type ? for help. Type -D to quit. Loading startup file "/home/eobr007/.magma.startup" Loading "code.m" Loading "sign.m" > > n := 6; > G := PermutationGroup ("3A6", 1); > for p in [2, 3, 5] do for> L := IrreducibleModules (G, GF(p)); for> L := [ActionGroup (x): x in L]; for> L := [x : x in L | #x eq #G]; for> "Degrees of faithful repns are ", [Degree (x): x in L]; for> f := ProcessReps (L, n); for> end for; Degrees of faithful repns are [ 6, 6, 18 ] Consider the following repn 1 Input degree = 6 Defining field size = 2 Order of generators [ 2, 4 ] Composition Factors of G is G | Alternating(6) * | Cyclic(3) 1 Vector space too small -- no regular orbit ======================================== Consider the following repn 2 Input degree = 6 Defining field size = 2 Order of generators [ 2, 4 ] Composition Factors of G is G | Alternating(6) * | Cyclic(3) 1 Vector space too small -- no regular orbit ======================================== Consider the following repn 3 Input degree = 18 Defining field size = 2 Order of generators [ 2, 4 ] Composition Factors of G is G | Alternating(6) * | Cyclic(3) 1 Refined bound on degree is 16 Over refined degree limit -- so G has regular orbit ======================================== Degrees of faithful repns are [] Degrees of faithful repns are [ 6, 12, 30 ] Consider the following repn 1 Input degree = 6 Defining field size = 5 Order of generators [ 2, 4, 4 ] Composition Factors of G is G | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 7 Order of G is 4320 ... #O is now 540 ... #O is now 2700 ... #O is now 4860 ... #O is now 7020 ... #O is now 7560 ... #O is now 8280 ... #O is now 10440 ... #O is now 11160 ... #O is now 12240 Proved no regular orbit ======================================== Consider the following repn 2 Input degree = 12 Defining field size = 5 Order of generators [ 2, 4, 4 ] Composition Factors of G is G | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | 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 = 30 Defining field size = 5 Order of generators [ 2, 4, 4 ] Composition Factors of G is G | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 19 Over refined degree limit -- so G has regular orbit ======================================== > > n := 6; > G := PermutationGroup ("6A6", 1); > for p in [2, 3, 5] do for> L := IrreducibleModules (G, GF(p)); for> L := [ActionGroup (x): x in L]; for> L := [x : x in L | #x eq #G]; for> "Degrees of faithful repns are ", [Degree (x): x in L]; for> f := ProcessReps (L, n); for> end for; Degrees of faithful repns are [] Degrees of faithful repns are [] Degrees of faithful repns are [ 12, 12 ] Consider the following repn 1 Input degree = 12 Defining field size = 5 Order of generators [ 4, 8, 4 ] Composition Factors of G is G | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 9 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 2 Input degree = 12 Defining field size = 5 Order of generators [ 4, 8, 4 ] Composition Factors of G is G | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 9 Over refined degree limit -- so G has regular orbit ======================================== > > n := 7; > G := PermutationGroup ("3A7", 1); > for p in [2, 3, 5, 7] do for> L := IrreducibleModules (G, GF(p)); for> L := [ActionGroup (x): x in L]; for> L := [x : x in L | #x eq #G]; for> "Degrees of faithful repns are ", [Degree (x): x in L]; for> f := ProcessReps (L, n); for> end for; Degrees of faithful repns are [ 12, 30, 48, 48 ] Consider the following repn 1 Input degree = 12 Defining field size = 2 Order of generators [ 3, 5 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) 1 Vector space too small -- no regular orbit ======================================== Consider the following repn 2 Input degree = 30 Defining field size = 2 Order of generators [ 3, 5 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) 1 Refined bound on degree is 25 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 3 Input degree = 48 Defining field size = 2 Order of generators [ 3, 5 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) 1 Refined bound on degree is 31 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 4 Input degree = 48 Defining field size = 2 Order of generators [ 3, 5 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) 1 Refined bound on degree is 31 Over refined degree limit -- so G has regular orbit ======================================== Degrees of faithful repns are [] Degrees of faithful repns are [ 6, 12, 30, 30, 36, 42 ] Consider the following repn 1 Input degree = 6 Defining field size = 5 Order of generators [ 3, 5, 4 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Vector space too small -- no regular orbit ======================================== Consider the following repn 2 Input degree = 12 Defining field size = 5 Order of generators [ 3, 5, 4 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | 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 = 30 Defining field size = 5 Order of generators [ 3, 5, 4 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 21 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 4 Input degree = 30 Defining field size = 5 Order of generators [ 3, 5, 4 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 19 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 5 Input degree = 36 Defining field size = 5 Order of generators [ 3, 5, 4 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 23 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 6 Input degree = 42 Defining field size = 5 Order of generators [ 3, 5, 4 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 25 Over refined degree limit -- so G has regular orbit ======================================== Degrees of faithful repns are [ 6, 6, 9, 9, 15, 15, 21, 21, 21, 21 ] Consider the following repn 1 Input degree = 6 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 7 Order of G is 15120 ... #O is now 7560 ... #O is now 15120 ... #O is now 22680 ... #O is now 24570 ... #O is now 32130 ... #O is now 39690 ... #O is now 47250 ... #O is now 51030 ... #O is now 58590 ... #O is now 60102 ... #O is now 63882 ... #O is now 65772 ... #O is now 68292 ... #O is now 70812 ... #O is now 74592 ... #O is now 82152 ... #O is now 84042 ... #O is now 84672 ... #O is now 86562 ... #O is now 94122 ... #O is now 96642 ... #O is now 97902 ... #O is now 101682 ... #O is now 104202 Proved no regular orbit ======================================== Consider the following repn 2 Input degree = 6 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 7 Order of G is 15120 ... #O is now 1512 ... #O is now 9072 ... #O is now 16632 ... #O is now 18522 ... #O is now 22302 ... #O is now 26082 ... #O is now 27972 ... #O is now 30492 ... #O is now 38052 ... #O is now 40572 ... #O is now 43092 ... #O is now 43722 ... #O is now 51282 ... #O is now 58842 ... #O is now 62622 ... #O is now 70182 ... #O is now 73962 ... #O is now 75852 ... #O is now 77742 ... #O is now 79254 ... #O is now 86814 ... #O is now 90594 ... #O is now 91224 ... #O is now 98784 ... #O is now 106344 Proved no regular orbit ======================================== Consider the following repn 3 Input degree = 9 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 8 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 4 Input degree = 9 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 8 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 5 Input degree = 15 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 11 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 6 Input degree = 15 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 11 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 7 Input degree = 21 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 15 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 8 Input degree = 21 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 14 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 9 Input degree = 21 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 15 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 10 Input degree = 21 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 14 Over refined degree limit -- so G has regular orbit ======================================== > > G := PermutationGroup ("6A7", 1); > for p in [2, 3] do for> L := IrreducibleModules (G, GF(p)); for> L := [ActionGroup (x): x in L]; for> L := [x : x in L | #x eq #G]; for> "Degrees of faithful repns are ", [Degree (x): x in L]; for> f := ProcessReps (L, n); for> end for; Degrees of faithful repns are [] Degrees of faithful repns are [] > > G := MatrixGroup ("6A7", 1); > p := 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 [ 12, 12, 24, 48 ] > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 12 Defining field size = 5 Order of generators [ 3, 5, 4 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 10 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 2 Input degree = 12 Defining field size = 5 Order of generators [ 3, 5, 4 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 10 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 3 Input degree = 24 Defining field size = 5 Order of generators [ 3, 5, 4 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 16 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 4 Input degree = 48 Defining field size = 5 Order of generators [ 3, 5, 4 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 28 Over refined degree limit -- so G has regular orbit ======================================== > > p := 7; > L := [MatrixGroup ("6A7", i): i in [9..11]]; > "Degrees of faithful repns are ", [Degree (x): x in L]; Degrees of faithful repns are [ 6, 6, 24 ] > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 6 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 6 Order of G is 15120 Found regular orbit ======================================== Consider the following repn 2 Input degree = 6 Defining field size = 7 Order of generators [ 3, 5, 6 ] Composition Factors of G is G | Alternating(7) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 6 Order of G is 15120 Found regular orbit ======================================== Consider the following repn 3 Input degree = 24 Defining field size = 7 Order of generators [ 3, 5, 6 ] 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 ======================================== > > n := 6; > G := PermutationGroup ("3S6", 1); > for p in [2, 3, 5] do for> L := IrreducibleModules (G, GF(p)); for> L := [ActionGroup (x): x in L]; for> L := [x : x in L | #x eq #G]; for> "Degrees of faithful repns are ", [Degree (x): x in L]; for> f := ProcessReps (L, n); for> end for; Degrees of faithful repns are [ 6, 6, 18 ] Consider the following repn 1 Input degree = 6 Defining field size = 2 Order of generators [ 2, 5 ] Composition Factors of G is G | Cyclic(2) * | Alternating(6) * | Cyclic(3) 1 Vector space too small -- no regular orbit ======================================== Consider the following repn 2 Input degree = 6 Defining field size = 2 Order of generators [ 2, 5 ] Composition Factors of G is G | Cyclic(2) * | Alternating(6) * | Cyclic(3) 1 Vector space too small -- no regular orbit ======================================== Consider the following repn 3 Input degree = 18 Defining field size = 2 Order of generators [ 2, 5 ] Composition Factors of G is G | Cyclic(2) * | Alternating(6) * | Cyclic(3) 1 Refined bound on degree is 17 Over refined degree limit -- so G has regular orbit ======================================== Degrees of faithful repns are [] Degrees of faithful repns are [ 6, 12, 30 ] Consider the following repn 1 Input degree = 6 Defining field size = 5 Order of generators [ 2, 5, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 7 Order of G is 8640 ... #O is now 4320 ... #O is now 5400 ... #O is now 6120 ... #O is now 10440 Proved no regular orbit ======================================== Consider the following repn 2 Input degree = 12 Defining field size = 5 Order of generators [ 2, 5, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | 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 = 30 Defining field size = 5 Order of generators [ 2, 5, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 19 Over refined degree limit -- so G has regular orbit ======================================== > > n := 6; > L := eval Read ("6S6-p5"); > "Degrees of faithful repns are ", [Degree (x): x in L]; Degrees of faithful repns are [ 12, 12 ] > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 12 Defining field size = 5 Order of generators [ 2, 5, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 10 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 2 Input degree = 12 Defining field size = 5 Order of generators [ 2, 5, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(6) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 10 Over refined degree limit -- so G has regular orbit ======================================== > > n := 7; > > G := PermutationGroup ("3S7", 1); > for p in [2, 3, 5, 7] do for> L := IrreducibleModules (G, GF(p)); for> L := [ActionGroup (x): x in L]; for> L := [x : x in L | #x eq #G]; for> "Degrees of faithful repns are ", [Degree (x): x in L]; for> f := ProcessReps (L, n); for> end for; Degrees of faithful repns are [ 12, 30, 96 ] Consider the following repn 1 Input degree = 12 Defining field size = 2 Order of generators [ 2, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) 1 Vector space too small -- no regular orbit ======================================== Consider the following repn 2 Input degree = 30 Defining field size = 2 Order of generators [ 2, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) 1 Refined bound on degree is 26 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 3 Input degree = 96 Defining field size = 2 Order of generators [ 2, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) 1 Refined bound on degree is 57 Over refined degree limit -- so G has regular orbit ======================================== Degrees of faithful repns are [] Degrees of faithful repns are [ 6, 12, 30, 30, 36, 42 ] Consider the following repn 1 Input degree = 6 Defining field size = 5 Order of generators [ 2, 6, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Vector space too small -- no regular orbit ======================================== Consider the following repn 2 Input degree = 12 Defining field size = 5 Order of generators [ 2, 6, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 12 Order of G is 60480 Found regular orbit ======================================== Consider the following repn 3 Input degree = 30 Defining field size = 5 Order of generators [ 2, 6, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 20 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 4 Input degree = 30 Defining field size = 5 Order of generators [ 2, 6, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 21 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 5 Input degree = 36 Defining field size = 5 Order of generators [ 2, 6, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 24 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 6 Input degree = 42 Defining field size = 5 Order of generators [ 2, 6, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 26 Over refined degree limit -- so G has regular orbit ======================================== Degrees of faithful repns are [ 12, 18, 30, 42, 42 ] Consider the following repn 1 Input degree = 12 Defining field size = 7 Order of generators [ 2, 6, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(3) 1 Refined bound on degree is 11 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 2 Input degree = 18 Defining field size = 7 Order of generators [ 2, 6, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 13 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 3 Input degree = 30 Defining field size = 7 Order of generators [ 2, 6, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 19 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 4 Input degree = 42 Defining field size = 7 Order of generators [ 2, 6, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 25 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 5 Input degree = 42 Defining field size = 7 Order of generators [ 2, 6, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 27 Over refined degree limit -- so G has regular orbit ======================================== > > n := 7; > L := eval Read ("6S7-p5"); > "Degrees of faithful repns are ", [Degree (x): x in L]; Degrees of faithful repns are [ 24, 12, 48, 12 ] > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 24 Defining field size = 5 Order of generators [ 2, 12, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 17 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 2 Input degree = 12 Defining field size = 5 Order of generators [ 2, 12, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | 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 = 48 Defining field size = 5 Order of generators [ 2, 12, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 29 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 4 Input degree = 12 Defining field size = 5 Order of generators [ 2, 12, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 11 Over refined degree limit -- so G has regular orbit ======================================== > > L := eval Read ("6S7-p7"); > "Degrees of faithful repns are ", [Degree (x): x in L]; Degrees of faithful repns are [ 48, 12, 12 ] > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 48 Defining field size = 7 Order of generators [ 2, 12, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(3) 1 Refined bound on degree is 27 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 2 Input degree = 12 Defining field size = 7 Order of generators [ 2, 12, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(3) 1 Refined bound on degree is 9 Over refined degree limit -- so G has regular orbit ======================================== Consider the following repn 3 Input degree = 12 Defining field size = 7 Order of generators [ 2, 12, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(7) * | Cyclic(3) * | Cyclic(2) * | Cyclic(3) 1 Refined bound on degree is 9 Over refined degree limit -- so G has regular orbit ======================================== Total time: 52.939 seconds, Total memory usage: 64.12MB