Supercharacter theories for groups of order 8

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Contents

This article gives specific information, namely, supercharacter theories, about a family of groups, namely: groups of order 8.
View supercharacter theories for group families | View supercharacter theories for groups of a particular order |View other specific information about groups of order 8
Group GAP ID second part Hall-Senior number Nilpotency class Supercharacter theories page
cyclic group:Z8 1 3 1 supercharacter theories for cyclic group:Z8
direct product of Z4 and Z2 2 2 1 supercharacter theories for direct product of Z4 and Z2
dihedral group:D8 3 4 2 supercharacter theories for dihedral group:D8
quaternion group 4 5 2 supercharacter theories for quaternion group
elementary abelian group:E8 5 1 1 supercharacter theories for elementary abelian group:E8

Summary

Group GAP ID second part Hall-Senior number Nilpotency class Total number of supercharacter theories Number of equivalence classes of supercharacter theories under the automorphism group action
cyclic group:Z8 1 3 1 9 9
direct product of Z4 and Z2 2 2 1  ?  ?
dihedral group:D8 3 4 2 9 7
quaternion group 4 5 2 9 5
elementary abelian group:E8 5 1 1  ?  ?