Group 8.7.8.0 of order 8


01234567
10325476
23016745
32107654
45670123
54761032
67452301
76543210

Centre:   0   1   2   3   4   5   6   7

Centrum:   0   1   2   3   4   5   6   7

Nucleus:   0   1   2   3   4   5   6   7

Left Nucleus:   0   1   2   3   4   5   6   7

Middle Nucleus:   0   1   2   3   4   5   6   7

Right Nucleus:   0   1   2   3   4   5   6   7

1 Element of order 1:   0

7 Elements of order 2:   1   2   3   4   5   6   7

Commutator Subloop:   0

Associator Subloop:   0

8 Conjugacy Classes of size 1:

Automorphic Inverse Property:   HOLDS

Al Property:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   8 (8, 8)


/ revised November, 2001