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(1,[[0,1,2,3]],[[0,1,2,3],[0,2,3,1],[0,3,1,2],[1,0,3,2],[1,2,0,3],[1,3,2,0],[2,0,1,3],[2,1,3,0],[2,3,0,1],[3,0,2,1],[3,1,0,2],[3,2,1,0]])
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(1,"iota_4^3",[])
(4,"iota_4^3",[[0,1,2],[0,2,1],[1,0,2],[1,2,0],[2,0,1],[2,1,0]])
(6,"iota_4^3",[[0,1,2],[0,1,3],[0,2,1],[0,3,1],[1,0,2],[1,0,3],[1,2,0],[1,3,0],[2,0,1],[2,1,0],[3,0,1],[3,1,0]])
(4,"iota_4^3",[[0,1,2],[0,1,3],[0,2,1],[0,2,3],[0,3,1],[0,3,2],[1,0,2],[1,0,3],[1,2,0],[1,3,0],[2,0,1],[2,0,3],[2,1,0],[2,3,0],[3,0,1],[3,0,2],[3,1,0],[3,2,0]])
(1,"iota_4^4",[])
(1,"rho_1",[])
(3,"rho_1",[[0,1,2,3],[0,2,1,3],[1,0,3,2],[1,3,0,2],[2,0,3,1],[2,3,0,1],[3,1,2,0],[3,2,1,0]])
(1,"rho_2",[])
(1,"rho_2",[[0,1,2,3],[0,1,3,2],[0,2,1,3],[0,2,3,1],[0,3,1,2],[0,3,2,1],[1,0,2,3],[1,0,3,2],[1,2,0,3],[1,2,3,0],[1,3,0,2],[1,3,2,0],[2,0,1,3],[2,0,3,1],[2,1,0,3],[2,1,3,0],[2,3,0,1],[2,3,1,0],[3,0,1,2],[3,0,2,1],[3,1,0,2],[3,1,2,0],[3,2,0,1],[3,2,1,0]])
(1,P_4 \cup C_\infty)
([14,416,505,144],[15,1],[4,2],[1],1102)