Right Bol Loop 16.7.4.72 of order 16


0123456789101112131415
1032765498111014151213
2301547610111513814912
3210674511101315912814
4756023115131214109118
5647201312148915111310
6574310214129813101511
7465132013151412118109
8912111510141347235160
9814101311121574326051
1011159128131456470312
1110138149151265741203
1214813101591123014675
1315111291410810653427
1412915111381032107546
1513101481211901562734

Centre:   0   4

Centrum:   0   1   4   7

Nucleus:   0   4

Left Nucleus:   0   1   4   7

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

7 Elements of order 2:   1   2   3   4   5   6   7

8 Elements of order 4:   8   9   10   11   12   13   14   15

Commutator Subloop:   0   4

Associator Subloop:   0   4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (2,5)(3,6) 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:   64 (1024, 2048)


/ revised October, 2001