Alternating Group

Even Permutation Groups $A_n$ which are Normal Subgroups of the Permutation Group of Order $n!/2$. They are Finite analogs of the families of simple Lie Groups. The lowest order alternating group is 60. Alternating groups with $n\geq 5$ are non-Abelian Simple Groups. The number of conjugacy classes in the alternating groups $A_n$ for $n=2$, 3, ... are 1, 3, 4, 5, 7, 9, ... (Sloane's A000702).

See also 15 Puzzle, Finite Group, Group, Lie Group, Simple Group, Symmetric Group

References

Sloane, N. J. A. Sequence A000702/M2307 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

Wilson, R. A. ``ATLAS of Finite Group Representation.'' http://for.mat.bham.ac.uk/atlas/html/contents.html#alt.