... (g 11 ,g 22) (g 33 ,g 44) (g 55).Throughout this paper, the c conjugacy classes of G will be denoted by C1, ,Cc.If g 1, ,g k∈ G, we define (g 1i1, ,g kik)tobeaCj-cycle if g k g k−1·· g 1∈ ... H is a subgroup of a group G, letA↑ G Hdenotethe induced representation of A to G. IfφA↑ G His the character of A↑ G H, then for anyτ ∈ G, φA↑ G H(τ)=1|H| g G φA (g −1 g) (13)where ... to give proofs of a varietyof generating functions for permutation statistics for Z2 Sn[1, 2].In 2000, Wagner described a natural extension of this λ-ring Frobenius characteristic for groups...