Group 20.1.2.0 of order 20

Centre:   0   16

Centrum:   0   16

Nucleus:   0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19

Left Nucleus:   0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19

Middle Nucleus:   0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19

Right Nucleus:   0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19

1 Element of order 1:   0

1 Element of order 2:   16

10 Elements of order 4:   1   2   3   4   5   6   7   8   9   10

4 Elements of order 5:   11   12   13   14

4 Elements of order 10:   15   17   18   19

Commutator Subloop:   0   11   12   13   14

Associator Subloop:   0

2 Conjugacy Classes of size 1:

•   0
•   16

4 Conjugacy Classes of size 2:

•   11   12
•   13   14
•   15   17
•   18   19

2 Conjugacy Classes of size 5:

•   1   2   3   4   5
•   6   7   8   9   10

Automorphic Inverse Property:   FAILS.   (1^-1)(3^-1) neq (1*3)^-1

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

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

Right (Left, Full) Mult Group Orders:   20 (20, 200)

/ revised November, 2001