HigmanSimsGroupHS (Built-in Mathematica Symbol)

HigmanSimsGroupHS[] represents the sporadic simple Higman\[Dash]Sims group HS.

JankoGroupJ2 (Built-in Mathematica Symbol)

JankoGroupJ2[] represents the sporadic simple Janko group J_2.

MathieuGroupM12 (Built-in Mathematica Symbol)

MathieuGroupM12[] represents the sporadic simple Mathieu group M_12.

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Power (Built-in Mathematica Symbol)

x^y gives x to the power y.

OrbitRepresentatives (Combinatorica Package Symbol)

OrbitRepresentatives[pg, x] returns a representative of each orbit of x induced by the action of the group pg on x.

CyclicGroupIndex (Combinatorica Package Symbol)

CyclicGroupIndex[n, x] returns the cycle index of the cyclic group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

DihedralGroupIndex (Combinatorica Package Symbol)

DihedralGroupIndex[n, x] returns the cycle index of the dihedral group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

SymmetricGroupIndex (Combinatorica Package Symbol)

SymmetricGroupIndex[n, x] returns the cycle index of the symmetric group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

Orbits (Combinatorica Package Symbol)

Orbits[pg, x] returns the orbits of x induced by the action of the group pg on x.