Ambivalent means that each element of the group A_n is a conjugate of its inverse element.

The only alternating groups A_n with real character table.

REFERENCES

G. James and A. Kerber, The Representation Theory of the Symmetric Group, Encyclopedia of Maths. and its Appls., Vol. 16, Addison-Wesley, 1981, Reading, MA, U.S.A., p. 12, 1.2.12 and p. 14, 1.2.16.