Skip to main content

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.