Group 24.3.4.0 of order 24


01234567891011121314151617181920212223
12305746913208231117221418162112151910
23017654131112910818191716141523222120
30126475118231320916211814172210191512
45762310141722162118132091182319101215
57643021171819141516111213891021202322
64571203161415181917910813111222232021
76450132181621172214823119132015121019
81013121517161920111392341822217142650
92011232218142112280131051619156173471
10131281719151612322003215472269181411
11239202114182210013281261715195161743
12810131615191732002321226742151114189
13128101916171523391112071421224180562
14221821201192319516617152812100137134
15171916131210842152267232132001411918
16151719101381222418714211112023395026
17191615128131021714418223923201116205
18211422239112015617516190131012284317
19161517810121372262154200312321891114
20112391821221421031210157561941316178
21142218920231161941575121021031613817
22182114112320951571946103201211781316
23920111422211801211032194651578171613

Centre:   0   2   5   6

Centrum:   0   2   5   6

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

3 Elements of order 2:   2   5   6

2 Elements of order 3:   13   20

12 Elements of order 4:   1   3   4   7   9   10   11   12   14   15   18   19

6 Elements of order 6:   8   16   17   21   22   23

Commutator Subloop:   0   13   20

Associator Subloop:   0

4 Conjugacy Classes of size 1:

4 Conjugacy Classes of size 2:

4 Conjugacy Classes of size 3:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-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, 144)


/ revised November, 2001