Dear Vipul Naik, dear all, here is the story of the bug you encountered in ExtensionRepresentatives: It actually was discovered by the GAP team in the past, and a fix was found -- in fact, this already happened in 2006! However, by accident this fix was not applied to the GAP 4.4.x series, so it never made it to end users.
The good part is, though, that I can tell you a fix, and that this problem will also be gone in the upcoming GAP 4.5.x series. Indeed, if you wanted to you could try the GAP 4.5 beta version (see <http://mail.gap-system.org/pipermail/forum/2011/003334.html>). In the meantime, though, you can manually fix your copy of GAP 4.4.12. The simplest way to do so is take attached file "grppcext.gi" and use that to replace the file of the same name in the "lib" directory of your GAP 4.4.12 installation. But I am not completely sure if this mailing list will let my attachment through. So here is how to manually apply the fix: Use a plain text editor (not MS Word!) to open the file "grppcext.gi" in the "lib" directory of the GAP directory. In there, lines 748 and following currently reads: elif Dimension( Image(cc.cohom)) = 1 then return [ExtensionSQ( cc.collector, G, M, 0 ), ExtensionSQ( cc.collector, G, M, Basis(Source(cc.cohom))[1])]; This needs to be replaced by: elif Dimension( Image(cc.cohom)) = 1 then c := Basis(Image(cc.cohom))[1]; c := PreImagesRepresentative(cc.cohom, c); return [ExtensionSQ( cc.collector, G, M, 0 ), ExtensionSQ( cc.collector, G, M, c )]; Best wishes, Max
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