[GAP Forum] Schur Multiplier

[Alexander Hulpke]

Dear GAP-Forum,

> I would like to ask that  how we can compute the Schur Multiplier of a given finite group by Gap.

Let me just add to Derek Holt's response, that GAP also has a built-in
routine for multiplier calcultation. The commands are
AbelianInvariantsMultiplier (structure of the multiplier) and
EpimorphismSchurCover (map from a covering group, represented as finitely
presented group, onto original group)

gap> AbelianInvariantsMultiplier(SymmetricGroup(6));
[ 2 ]
gap> EpimorphismSchurCover(SymmetricGroup(6));
[ f1, f2, f3, f4, f5 ] -> [ (1,2), (2,3), (3,4), (4,5), (5,6) ]

The algorithms used are similar to the ones used by the `cohomolo' package,
the main advantage of the library implementation is that it does not require
an external program and thus can also run under Windows or if the `cohomolo'
package is not installed. On the other hand I would expect the `cohomolo'
package to run faster.

Best wishes,

   Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke