Right Bol Loop 16.7.4.18 of order 16

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

Centre: 0 2

Centrum: 0 2 6 7

Nucleus: 0 2

Left Nucleus: 0 2 6 7

Middle Nucleus: 0 2

Right Nucleus: 0 2

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: 2 6 7 8 11 14 15

8 Elements of order 4: 1 3 4 5 9 10 12 13

Commutator Subloop: 0 2 6 7

Associator Subloop: 0 2 6 7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

1 3 4 5
8 11 14 15
9 10 12 13

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

A_l Property: FAILS. The left inner mapping L_1,8 = (4,5)(6,7)(8,11)(9,10)(12,13)(14,15) is not an automorphism. L_1,8(4*8) neq L_1,8(4)*L_1,8(8)

A_r Property: FAILS. The right inner mapping R_1,8 = (1,5)(3,4)(8,11)(9,13)(10,12)(14,15) is not an automorphism. R_1,8(8*1) neq R_1,8(8)*R_1,8(1)

Right (Left, Full) Mult Group Orders: 64 (4096, 16384)

/ revised October, 2001

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

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

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