Right Bol Loop 16.11.2.26 of order 16

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	7	6	5	4	9	15	11	13	8	14	10	12
2	3	0	1	6	7	4	5	10	11	15	12	14	8	9	13
3	2	1	0	5	4	7	6	11	13	12	8	10	9	15	14
4	7	6	5	0	3	2	1	15	12	13	14	9	10	11	8
5	6	7	4	3	0	1	2	14	10	9	15	13	12	8	11
6	5	4	7	2	1	0	3	13	14	8	9	11	15	12	10
7	4	5	6	1	2	3	0	12	8	14	10	15	11	13	9
8	12	13	14	15	11	10	9	4	7	6	5	1	2	3	0
9	15	14	13	12	10	11	8	7	0	5	2	4	3	6	1
10	14	15	12	13	9	8	11	6	5	0	1	3	4	7	2
11	13	12	15	14	8	9	10	5	2	1	4	6	7	0	3
12	8	11	10	9	13	14	15	1	4	3	6	0	5	2	7
13	11	8	9	10	12	15	14	2	3	4	7	5	0	1	6
14	10	9	8	11	15	12	13	3	6	7	0	2	1	4	5
15	9	10	11	8	14	13	12	0	1	2	3	7	6	5	4

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 9 10 12 13

4 Elements of order 4: 8 11 14 15

Commutator Subloop: 0 4

Associator Subloop: 0 4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

1 7
2 6
3 5
8 15
9 12
10 13
11 14

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

A_l Property: FAILS. The left inner mapping L_1,8 = (2,6)(3,5)(8,15)(9,12)(10,13)(11,14) is not an automorphism. L_1,8(2*8) neq L_1,8(2)*L_1,8(8)

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

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

/ revised October, 2001

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	7	6	5	4	9	15	11	13	8	14	10	12
2	3	0	1	6	7	4	5	10	11	15	12	14	8	9	13
3	2	1	0	5	4	7	6	11	13	12	8	10	9	15	14
4	7	6	5	0	3	2	1	15	12	13	14	9	10	11	8
5	6	7	4	3	0	1	2	14	10	9	15	13	12	8	11
6	5	4	7	2	1	0	3	13	14	8	9	11	15	12	10
7	4	5	6	1	2	3	0	12	8	14	10	15	11	13	9
8	12	13	14	15	11	10	9	4	7	6	5	1	2	3	0
9	15	14	13	12	10	11	8	7	0	5	2	4	3	6	1
10	14	15	12	13	9	8	11	6	5	0	1	3	4	7	2
11	13	12	15	14	8	9	10	5	2	1	4	6	7	0	3
12	8	11	10	9	13	14	15	1	4	3	6	0	5	2	7
13	11	8	9	10	12	15	14	2	3	4	7	5	0	1	6
14	10	9	8	11	15	12	13	3	6	7	0	2	1	4	5
15	9	10	11	8	14	13	12	0	1	2	3	7	6	5	4

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	7	6	5	4	9	15	11	13	8	14	10	12
2	3	0	1	6	7	4	5	10	11	15	12	14	8	9	13
3	2	1	0	5	4	7	6	11	13	12	8	10	9	15	14
4	7	6	5	0	3	2	1	15	12	13	14	9	10	11	8
5	6	7	4	3	0	1	2	14	10	9	15	13	12	8	11
6	5	4	7	2	1	0	3	13	14	8	9	11	15	12	10
7	4	5	6	1	2	3	0	12	8	14	10	15	11	13	9
8	12	13	14	15	11	10	9	4	7	6	5	1	2	3	0
9	15	14	13	12	10	11	8	7	0	5	2	4	3	6	1
10	14	15	12	13	9	8	11	6	5	0	1	3	4	7	2
11	13	12	15	14	8	9	10	5	2	1	4	6	7	0	3
12	8	11	10	9	13	14	15	1	4	3	6	0	5	2	7
13	11	8	9	10	12	15	14	2	3	4	7	5	0	1	6
14	10	9	8	11	15	12	13	3	6	7	0	2	1	4	5
15	9	10	11	8	14	13	12	0	1	2	3	7	6	5	4

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	7	6	5	4	9	15	11	13	8	14	10	12
2	3	0	1	6	7	4	5	10	11	15	12	14	8	9	13
3	2	1	0	5	4	7	6	11	13	12	8	10	9	15	14
4	7	6	5	0	3	2	1	15	12	13	14	9	10	11	8
5	6	7	4	3	0	1	2	14	10	9	15	13	12	8	11
6	5	4	7	2	1	0	3	13	14	8	9	11	15	12	10
7	4	5	6	1	2	3	0	12	8	14	10	15	11	13	9
8	12	13	14	15	11	10	9	4	7	6	5	1	2	3	0
9	15	14	13	12	10	11	8	7	0	5	2	4	3	6	1
10	14	15	12	13	9	8	11	6	5	0	1	3	4	7	2
11	13	12	15	14	8	9	10	5	2	1	4	6	7	0	3
12	8	11	10	9	13	14	15	1	4	3	6	0	5	2	7
13	11	8	9	10	12	15	14	2	3	4	7	5	0	1	6
14	10	9	8	11	15	12	13	3	6	7	0	2	1	4	5
15	9	10	11	8	14	13	12	0	1	2	3	7	6	5	4