Group 21.2.21.0 of order 21


01234567891011121314151617181920
14026359101112137818142019171615
20351641213789101115201918141716
32560411011121378920161714151819
46105231112137891017181516192014
53642108910111213716191815201417
65413021378910111219171420161518
79121011813161820171519141036452
81013111297182017151914163540216
91171213108201715191416184125630
10128137119171519141618202361045
11139781210151914161820176403521
12710891311191416182017150254163
13811910712141618201715195612304
14181520171619134260581391210711
15142016181917051342613117108129
16201917151814342605197101311812
17191814161520605134212101397118
18171415192016426051310811712913
19161718201415513426071281191310
20151619141718260513411912813107

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

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

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

2 Elements of order 3:   13   19

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

12 Elements of order 21:   7   8   9   10   11   12   14   15   16   17   18   20

Commutator Subloop:   0

Associator Subloop:   0

21 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:   21 (21, 21)


/ revised November, 2001