Right Bol Loop 16.11.2.137 of order 16


0123456789101112131415
1032765491514108111312
2301674510111512148913
3210547611139151012814
4765032115121314910118
5674301214101281391511
6547210313148911151210
7456123012811131514109
8121311151410941657230
9151410121311874360521
1014159131281163015472
1113128141591056702143
1281113910141510524367
1311812109151425473016
1410915118121332146705
1591014811131207231654

Centre:   0   4

Centrum:   0   4

Nucleus:   0   4

Left Nucleus:   0   4

Middle Nucleus:   0   4

Right Nucleus:   0   4


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets.


1 Element of order 1:   0

11 Elements of order 2:   1   2   3   4   5   6   7   10   11   13   14

4 Elements of order 4:   8   9   12   15

Commutator Subloop:   0   4

Associator Subloop:   0   4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (2-1)(9-1) neq (2*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (10,13)(11,14) is not an automorphism.   L1,8(2*8) neq L1,8(2)*L1,8(8)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   128 (1024, 2048)


/ revised October, 2001