Supercharacter theories for symmetric groups

From Groupprops
Jump to: navigation, search
This article gives specific information, namely, supercharacter theories, about a family of groups, namely: symmetric groups.
View supercharacter theories for group families | View other specific information about symmetric groups

This page discusses the supercharacter theories for symmetric groups.

Particular cases

n n! (order of symmetric group) Symmetric group S_n Is A_n simple? Is S_n complete? Number of supercharacter theories Supercharacter theory page
1 1 trivial group No Yes 1 --
2 2 cyclic group:Z2 No Yes 1 --
3 6 symmetric group:S3 Yes Yes 2 supercharacter theories for symmetric group:S3
4 24 symmetric group:S4 No Yes 5 supercharacter theories for symmetric group:S4
5 120 symmetric group:S5 Yes Yes 3 (at least!) supercharacter theories for symmetric group:S5
6 720 symmetric group:S6 Yes No 5 (at least!) supercharacter theories for symmetric group:S6
7 5040 symmetric group:S7 Yes Yes 3 (at least!) supercharacter theories for symmetric group:S7