[GAP Forum] coclass 2-groups

[Bettina Eick]

Dear Sidhartha,

starting from your presentation, you can do the following:

# define your group as fp-group in GAP
F := FreeGroup(3); x1 := F.1; x2 := F.2; y := F.3;
r := [x1^8, x2^8, y^4/(x2^4), x1^y/(x1*x2), x2^y/(x1^-2*x2^3), Comm(x2,x1)];
G := F/r;

# get a pc-presentation for your group
H := Image(EpimorphismQuotientSystem(PQuotient(G,2,6)));

# identify it in the SmallGroups Library
l := IdGroup(H);

This yields l = [256, 519] and it means that your group is
isomorphic to SmallGroup(256, 519).

Best wishes,
              Bettina