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Mar 13, 2016 at 14:16 history edited user31159 CC BY-SA 3.0
tl;dr updated. Minor corrections.
Mar 13, 2016 at 13:42 history edited user31159 CC BY-SA 3.0
One example removed, another added. Minor corrections.
Mar 13, 2016 at 13:27 comment added user31159 @Rainer You can find it in the "Details" section of FiniteGroupData, second Table. Three special group specifications are shown: "AbelianGroup", "DirectProduct" and "SemidirectProduct".
Mar 13, 2016 at 9:36 comment added Rainer one additional item @Xavier. Where did you find the FiniteGroupData command syntax on the DirectProduct? I checked with the MMA documentation and did not find it there....
Mar 13, 2016 at 9:16 comment added Rainer I was not aware of the DirectProduct Property in Finite GroupData. It seems that this is covering even very high order of abstract groups. If I try it with AlternatingGroup of degree 10 and CyclicGroup of degree 2 I get the correct order of 3628800. I'll try out if I find any combination of abstract groups which is not covered with this, but it seems that FiniteGroupData does the trick, thanks!
Mar 13, 2016 at 9:13 vote accept Rainer
Mar 13, 2016 at 2:48 history edited user31159 CC BY-SA 3.0
Alternative added.
Mar 13, 2016 at 2:20 history edited user31159 CC BY-SA 3.0
Added alternative code and comment.
Mar 13, 2016 at 2:14 history edited user31159 CC BY-SA 3.0
Added alternative code and comment.
Mar 13, 2016 at 0:48 history answered user31159 CC BY-SA 3.0