Group 24.9.1.1 of order 24


01234567891011121314151617181920212223
12305913411712181915614810161721232022
23019715518419161714136111281023222120
30127414916517810615131819111222202321
46108016113320217147122251121239181519
51312111821502131064192091823227161417
61084162070171314212322112325111819915
71417163180622211915910234820215111312
84610130122051611321227212317141591918
91519182113141230121351721716222048610
10846201322162102351112711714321915189
11513121511921981803220423221061471716
12115132115208231229181942106031714167
13121158214110156232220219039181617714
14171671822931961520212301021481112513
15191891123521214132220213171071681046
16714176310224188210239202119151351211
17167142262318203214810901915211213115
18915191421723711161032152220121364108
19189152314211122220716175312131010684
20222321101781261941471611181351590312
21202223121011191317564818161591471023
22232120171916101412715918811641353201
23212022191218171510913511168147642130

Centre:   0

Centrum:   0

Nucleus:   0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19   20   21   22   23

Left Nucleus:   0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19   20   21   22   23

Middle Nucleus:   0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19   20   21   22   23

Right Nucleus:   0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19   20   21   22   23

1 Element of order 1:   0

9 Elements of order 2:   2   4   11   14   19   20   21   22   23

8 Elements of order 3:   5   6   7   8   12   15   17   18

6 Elements of order 4:   1   3   9   10   13   16

Commutator Subloop:   0   2   5   6   7   8   12   15   17   18   20   23

Associator Subloop:   0

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 3:

2 Conjugacy Classes of size 6:

1 Conjugacy Class of size 8:

Automorphic Inverse Property:   FAILS.   (1-1)(5-1) neq (1*5)-1

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:   24 (24, 576)


/ revised November, 2001