On Mon, Aug 20, 2012 at 03:00:45PM +0800, R.E. Boss wrote: > What can I conclude from the equal structure descriptions below I stumbled > upon? > > gap> StructureDescription(SmallGroup(64,156)); > "Q8 : Q8" there is a normal subgroup Q_8 (the group of quaternions), and the quotient of your group over it is isomorphic to Q_8, and the extension is split. > gap> StructureDescription(SmallGroup(64,158)); > "Q8 : Q8" same as above, but the extension is different. > > gap> StructureDescription(SmallGroup(64,155)); > "(C8 : C4) : C2" there is a normal subgroup C_8:C_4 (a split extension of C_8 by C_4) on which C_2 acts nontrivially (C_k denotes the cyclic group of order k). > > gap> StructureDescription(SmallGroup(64,157)); > "(C8 : C4) : C2" as above, but some of the extensions involved are different. > > gap> StructureDescription(SmallGroup(64,159)); > "(C8 : C4) : C2" ditto. > > gap> StructureDescription(SmallGroup(64,160)); > "(C2 x C2) . (C2 x D8) = (C4 x C2) . (C2 x C2 x C2)" there are normal subgroups C_2xC_2 and C_4xC_2. The whole group can be described in two ways: 1) as a (possibly non-split) extension of C_2xC_2 by C_2xC_8 1) as a (possibly non-split) extension of C_4xC_2 by C_2xC_2xC_2.
I hope this gives you an idea... Best, Dmitrii CONFIDENTIALITY:This email is intended solely for the person(s) named and may be confidential and/or privileged.If you are not the intended recipient,please delete it,notify us and do not copy,use,or disclose its content. Towards A Sustainable Earth:Print Only When Necessary.Thank you. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
