Group 24.9.2.3 of order 24


01234567891011121314151617181920212223
12305911410768141513121918161722232120
23019785641110131215141716191821202322
30127410911586151412131819171623222021
46980131123217167521201110222315141819
51171011521403181949232286212012131617
69841321601712132120572322111018191415
71051131401521191894222368202113121716
84691201721613312021752223101119181514
98462123131016175720211011232214151918
10511714118319150222234921206817161213
11710515319118142023229420218616171312
12171316821420962322201819131514571011
13161217620921482223021918311415751110
14181519102352271120213116172012139468
15191418112272351021201317160213124986
16121713208236222194191820151431111057
17131612216228232049181902141513101175
18151914231121102022571617131312206849
19141815221020112123751716311213028694
20232122161812191317141568101149570231
21222023171913181216151486111094752013
22202321191614171518131211106857941302
23212220181715161419121310118675493120

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

9 Elements of order 2:   2   4   9   10   11   20   21   22   23

2 Elements of order 3:   15   16

6 Elements of order 4:   1   3   12   13   18   19

6 Elements of order 6:   5   6   7   8   14   17

Commutator Subloop:   0   2   14   15   16   17

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)(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, 288)


/ revised November, 2001