Magma V2.20-10 Thu Dec 11 2014 23:20:22 on mathcompprd01 [Seed = 2638530214] Type ? for help. Type -D to quit. Loading startup file "/home/eobr007/.magma.startup" Loading "code.m" Loading "sign.m" > > n := 5; > > p := 3; > G := eval Read ("minus-cover-s5-3"); > 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 [ 4, 12 ] > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 4 Defining field size = 3 Order of generators [ 4, 4, 4, 4, 2 ] Composition Factors of G is G | Cyclic(2) * | Alternating(5) * | 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 [ 4, 4, 4, 4, 2 ] Composition Factors of G is G | Cyclic(2) * | Alternating(5) * | Cyclic(2) 1 Refined bound on degree is 8 Over refined degree limit -- so G has regular orbit ======================================== > > p := 5; > G := eval Read ("minus-cover-s5-5"); > 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 [ 4, 8 ] > > // 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 = 4 Defining field size = 5 Order of generators [ 4, 4, 4, 4, 4, 2 ] Composition Factors of G is G | Cyclic(2) * | Alternating(5) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 5 Order of G is 480 ... #O is now 240 Proved 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 = 5 Order of generators [ 4, 4, 4, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(5) * | Cyclic(2) 1 Refined bound on degree is 4 Order of G is 240 Found regular orbit ======================================== Consider the following repn 1 Input degree = 8 Defining field size = 5 Order of generators [ 4, 4, 4, 4, 4, 2 ] Composition Factors of G is G | Cyclic(2) * | Alternating(5) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 7 Over refined degree limit -- so G has regular orbit ======================================== > Total time: 0.580 seconds, Total memory usage: 32.09MB