Journal of Integer Sequences, Vol. 16 (2013), Article 13.5.8

Integer Sequences Realized by the Subgroup Pattern of the Symmetric Group

L. Naughton and G. Pfeiffer
School of Mathematics
Applied Mathematics and Statistics
National University of Ireland


The subgroup pattern of a finite group G is the table of marks of G together with a list of representatives of the conjugacy classes of subgroups of G. In this article we describe a collection of sequences realized by the subgroup pattern of the symmetric group.

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(Concerned with sequences A000041 A000088 A000638 A001349 A005226 A005432 A018783 A029725 A029726 A051625 A051636 A062297 A116653 A200976 A216967 A218909 A218910 A218911 A218912 A218913 A218914 A218915 A218916 A218917 A218918 A218919 A218920 A218921 A218922 A218923 A218924 A218925 A218926 A218927 A218928 A218929 A218930 A218931 A218932 A218933 A218934 A218935 A218936 A218937 A218938 A218939 A218940 A218941 A218942 A218943 A218944 A218945 A218946 A218947 A218948 A218949 A218950 A218951 A218952 A218953 A218954 A218955 A218956 A218957 A218958 A218959 A218960 A218961 A218962 A218963 A218964 A218965 A218966 A218967 A218968 A218969 A218970 A218971 A218972 A218973 A218974 A218975.)

Received November 28 2012; revised version received May 20 2013. Published in Journal of Integer Sequences, June 4 2013.

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