RankPermutation[p] gives the rank of permutation p in lexicographic order.
SignaturePermutation[p] gives the signature of permutation p.
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ConwayGroupCo3[] represents the sporadic simple Conway group Co_3.
JankoGroupJ1[] represents the sporadic simple Janko group J_1.
McLaughlinGroupMcL[] represents the sporadic simple McLaughlin group McL.
Set
(Built-in Mathematica Symbol) lhs = rhs evaluates rhs and assigns the result to be the value of lhs. From then on, lhs is replaced by rhs whenever it appears. {l_1, l_2, ...} = {r_1, r_2, ...} evaluates ...
MultiplicationTable[l, f] constructs the complete transition table defined by the binary relation function f on the elements of list l.
PairGroupIndex[g, x] returns the cycle index of the pair group induced by g as a polynomial in x[1], x[2], ....PairGroupIndex[ci, x] takes the cycle index ci of a group g ...
Index
(Combinatorica Package Symbol) Index[p] gives the index of permutation p, the sum of all subscripts j such that p[[j]] is greater than p[[j + 1]].