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Table 1 Details of the conjugacy classes of some permutation groups needed in the proof of Proposition 20

From: The space of phylogenetic mixtures for equivariant models

G S 4 M Representatives of conj. classes C(G) χ C ( G ) n
〈(A T)(C G)〉 SSM {e,(A T)(C G)} (1,1) (4n,0)
〈(A C)(G T),(A G)(C T)〉 K81 {e,(A T)(C G),(A C)(G T),(A G)(C T)} (1,1,1,1) (4n,0,0,0)
〈(A C G T),(A G)〉 K80 {e,(A C)(G T),(A G)(C T),(A C G T),(A G)} (1,2,1,2,2) (4n,0,0,0,2n)
S 4 JC69 {e,(A C)(G T),(A C G T),(A G),(A C G)} (1,3,6,6,8) (4n,0,0,2n,1)
  1. For each permutation group in the column on the left, the corresponding equivariant model and conjugacy classes are described. For each conjugacy class, we give a list of representatives, its cardinality and the value taken by the character χnon it.