Group 24.7.2.8 of order 24


01234567891011121314151617181920212223
12503471316621911121820171419823221510
25410313121772269111923141881610152021
30145296191123121371722816141815102120
43052111918122013761621198171422231015
54321012111413157698101819161721202322
68151014121632022721823211109513141719
71620211811170231513519102291641223148
81512610143230164222185192113201917117
91922231713841521611420101231127051618
10681412152216132191823391720021511741
11182120167195221090171523134121632814
12141015861822123113162220751309411917
13172322199141102012482115627311501816
14106121582225181233160413209211719711
15121486102318931716222131921520071114
16201172118010117315519426221223814913
17239132219121214020483571511101618612
18217112016515419210017131223622148139
19221392317420385211142011107151816126
20111816721101960141715512822423113923
21716181120151712581910061423122491332
22131719923201411416821171810215361205
23919171322218711814204111615310212650

Centre:   0   5

Centrum:   0   5

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

7 Elements of order 2:   5   7   8   11   14   22   23

8 Elements of order 3:   2   4   6   13   15   16   19   21

8 Elements of order 6:   1   3   9   10   12   17   18   20

Commutator Subloop:   0   11   14   23

Associator Subloop:   0

2 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 3:

4 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(7-1) neq (1*7)-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