Right Bol Loop 16.11.2.226 of order 16

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

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

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