def sigmaGr(G):
    return sum([len(U.list()) for U in (G.subgroups())])

def wordLen(g):
    return g.length()

def HG(G):
    return sum([1/(wordLen(g)+1) for g in G.list()])

def LG(G):
    H = HG(G)
    return (H+exp(H)*log(H)).N()

for n in range(1,6):
    G = SymmetricGroup(n)
    print sigmaGr(G),LG(G)