Group 24.13.2.4 of order 24


01234567891011121314151617181920212223
12305746911810131512142019162223172118
23017654111098151413122322202118191716
30126475108119141215131821231716221920
45768910110132162018231712211319141522
57649118101203202316181913171522121421
64571081193021181623202114221217151319
76451110982310231820162215191421131217
89111001324567171921221216142013182315
91110812035746192217211320122315161814
10891130216475211722191418151612232013
11108923107654222119171523131814201612
12141513172119221618202303128496105711
13121415191722212016231810239511487610
14151312212217191823162032011068711459
15131214221921172320181621301171059648
16182320121413151721192246570811039112
17212219161820231214131581091140536127
18232016141512132122171967453100112891
19172122201623181312151498111051704236
20161823131215141917222154761928011103
21221917182316201415121310118963427015
22191721232018161513141211910872615304
23201618151314122219211775642113911080

Centre:   0   2

Centrum:   0   2

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

13 Elements of order 2:   2   12   13   14   15   16   17   18   19   20   21   22   23

2 Elements of order 3:   4   8

2 Elements of order 4:   1   3

2 Elements of order 6:   7   11

4 Elements of order 12:   5   6   9   10

Commutator Subloop:   0   2   4   7   8   11

Associator Subloop:   0

2 Conjugacy Classes of size 1:

5 Conjugacy Classes of size 2:

2 Conjugacy Classes of size 6:

Automorphic Inverse Property:   FAILS.   (1-1)(13-1) neq (1*13)-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, 288)


/ revised November, 2001