If I type
?CycleIndex
I get
Information::notfound: Symbol CycleIndex not found. >>
If I then type
Needs["Combinatorica`"]
I get
General::compat: Combinatorica Graph and Permutations functionality has been superseded by preloaded functionaliy. The package now being loaded may conflict with this. Please see the Compatibility Guide for details.
Is there any good way to get the functionality I need without causing a conflict? The warning is somewhat strong and suggests nonspecific breakdowns further down the line...

FiniteGroupDataand related functions in Group Theory. For named groups, you can simply do something likeFiniteGroupData["Quaternion", "CycleIndex"]. In fact, I had this as an answer, but I don't know enough about the subject to decide whether that answers your question or not. Let me know if it helped and I'll make it an answer. – rm -rf♦ Oct 19 '12 at 19:54