Dear Alexander, Dear GAP team Thank you for response, i realize for my group since its a large group the process works partially, my group G=N:Q is a split extension of N by Q,where Q is an elementary abelian group.Subjecting the Permutation Representation of the Group G to the above process, Am able to generate Q(The acting Algebra) and not G.Is there a way i can proceed to get the matrix generators of N of same dimension as that of Q?Please.Regards David.Sent from Yahoo Mail on Android On Thu, 27 Aug 2020 at 19:59, Hulpke,Alexander<alexander.hul...@colostate.edu> wrote: Dear Forum, Dear David Musyoka,
[it turns out the question is to find a particular irreducible matrix representation.] > I have a permutation representation of a group G, and my intention is to get > the generators of the group in Matrix form over GF(3), What you can do generically is to use `IrreducibleRepresentations` to calculate the irreducible representations over a given field up to equivalence. For example, say I want a 42 dimensional representation of the given group: gap> g:=Group( (1,22,15,23)(2,14,18,7)(3,6)(4,24)(5,16,17,9)(8,13,20,11)(10,12)(19,21), > >(1,8)(2,3)(4,11)(5,13)(6,24)(7,12)(9,23)(10,16)(14,15)(17,20)(18,19)(21,22));; gap> StructureDescription(g); "(C2 x C2 x C2 x C2 x C2 x C2) : (PSL(3,2) x S3)” gap> reps:=IrreducibleRepresentations(g,GF(3));; gap> List(reps,x->DegreeOfMatrixGroup(Range(x))); [ 1, 1, 6, 6, 6, 6, 7, 7, 21, 21, 21, 21, 42, 42, 63, 63, 63, 63, 126, 126 ] gap> myrep:=First(reps,x->DegreeOfMatrixGroup(Range(x))=42); [ (1,22,15,23)(2,14,18,7)(3,6)(4,24)(5,16,17,9)(8,13,20,11)(10,12)(19,21), (1,8)(2,3)(4,11)(5,13)(6,24)(7,12)(9,23)(10,16)(14,15)(17,20)(18,19)(21,22) ] -> [ < immutable compressed matrix 42x42 over GF(3) >, < immutable compressed matrix 42x42 over GF(3) > ] gap> matg:=Group(MappingGeneratorsImages(myrep)[2]); <matrix group with 2 generators> gap> Size(matg); 64512 This is clearly limited by the group order and the dimensions of the representations — for larger groups this quickly becomes a research level problem. Also make sure you use GAP 4.11, as this has a better algorithm implemented. Best, Alexander Hulpke -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hul...@colostate.edu, http://www.math.colostate.edu/~hulpke _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
