[ifrphnja] Clock with generators of 13

The generators of GF(13) are 2, 6, 7, and 11, or equivalently, ±2 and ±6, or equivalently, ±2^±1. Here are their powers, with patterns visible. (Also multiplication and division.)

Generator	g^0	g^1	g^2	g^3	g^4	g^5	g^6	g^7	g^8	g^9	g^10	g^11	g^12
2	1	2	4	8	3	6	12	11	9	5	10	7	1
11	1	11	4	5	3	7	12	2	9	8	10	6	1
6	1	6	10	8	9	2	12	7	3	5	4	11	1
7	1	7	10	5	9	11	12	6	3	8	4	2	1

They are a permutation of 1 through 12. Create a clock with the digits permuted according to a generator. One vague idea is that the clock goes twice as fast every hour.

61 is also prime with generator 2.