Group 21.14.1.2 of order 21


01234567891011121314151617181920
14026358910111213716192014151718
20351641378910111217181419201516
32560411213789101119201715161814
46105239101112137820171816191415
53642101112137891015161918142017
65413021011121378918141520171619
79121011813161819142015173206514
81013111297201517161819142015346
91171213108181914201517160143265
10128137119151716181914201462053
11139781210191420151716184650132
12710891311171618191420156531420
13811910712142015171618195324601
14151817162019260513491113127810
15161418191720605134213810911127
16191514201817051342610127138911
17182019141615342605181012111379
18141720151916426051312798101113
19201615171418513426079111012138
20171916181514134260511138791012

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

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

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

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

1 Element of order 1:   0

14 Elements of order 3:   7   8   9   10   11   12   13   14   15   16   17   18   19   20

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

Commutator Subloop:   0   1   2   3   4   5   6

Associator Subloop:   0

1 Conjugacy Class of size 1:

2 Conjugacy Classes of size 3:

2 Conjugacy Classes of size 7:

Automorphic Inverse Property:   FAILS.   (1-1)(8-1) neq (1*8)-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:   21 (21, 441)


/ revised November, 2001