Magma V2.20-10 Thu Nov 13 2014 12:51:41 on mathcompprd01 [Seed = 2493975501] Type ? for help. Type -D to quit. Loading startup file "/home/eobr007/.magma.startup" Loading "code.m" Loading "sign.m" > > n := 8; > > p := 3; > G := eval Read ("minus-cover-s8-3"); > H := SecondCover (G); G | Cyclic(2) * | Alternating(8) * | Cyclic(2) 1 > L := [G, H]; > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 8 Defining field size = 3 Order of generators [ 4, 4, 4, 4, 4, 4, 4, 2 ] Composition Factors of G is G | Cyclic(2) * | Alternating(8) * | Cyclic(2) 1 Vector space too small -- no regular orbit ======================================== Consider the following repn 2 Input degree = 8 Defining field size = 3 Order of generators [ 4, 4, 4, 4, 4, 4, 4, 2 ] Composition Factors of G is G | Cyclic(2) * | Alternating(8) * | Cyclic(2) 1 Vector space too small -- no regular orbit ======================================== > > > > p := 5; > G := eval Read ("minus-cover-s8-5"); > H := SecondCover (G); G | Cyclic(2) * | Alternating(8) * | Cyclic(2) 1 > L := [G, H]; > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 8 Defining field size = 5 Order of generators [ 4, 4, 4, 4, 4, 4, 4, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(8) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 9 Order of G is 161280 ... #O is now 80640 ... #O is now 94080 ... #O is now 120960 ... #O is now 134400 ... #O is now 188160 ... #O is now 215040 ... #O is now 241920 Proved no regular orbit ======================================== Consider the following repn 2 Input degree = 8 Defining field size = 5 Order of generators [ 4, 4, 4, 4, 4, 4, 4, 4 ] Composition Factors of G is G | Cyclic(2) * | Alternating(8) * | Cyclic(2) * | Cyclic(2) 1 Refined bound on degree is 9 Order of G is 161280 ... #O is now 13440 ... #O is now 94080 ... #O is now 120960 ... #O is now 128640 ... #O is now 138720 ... #O is now 165600 ... #O is now 246240 Proved no regular orbit ======================================== > > > > p := 7; > G := eval Read ("minus-cover-s8-7"); > H := SecondCover (G); G | Cyclic(2) * | Alternating(8) * | Cyclic(2) 1 > L := [G, H]; > f := ProcessReps (L, n); Consider the following repn 1 Input degree = 8 Defining field size = 7 Order of generators [ 4, 4, 4, 4, 4, 4, 4, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(8) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 9 Order of G is 241920 ... #O is now 120960 ... #O is now 241920 ... #O is now 362880 ... #O is now 443520 Found regular orbit ======================================== Consider the following repn 2 Input degree = 8 Defining field size = 7 Order of generators [ 4, 4, 4, 4, 4, 4, 4, 6 ] Composition Factors of G is G | Cyclic(2) * | Alternating(8) * | Cyclic(3) * | Cyclic(2) 1 Refined bound on degree is 9 Order of G is 241920 Found regular orbit ======================================== > Total time: 10.300 seconds, Total memory usage: 125.94MB