Element structure of groups of order 243

Order statistics

FACTS TO CHECK AGAINST:

ORDER STATISTICS (cf. order statistics, order statistics-equivalent finite groups): number of nth roots is a multiple of n | Finite abelian groups with the same order statistics are isomorphic | Lazard Lie group has the same order statistics as the additive group of its Lazard Lie ring | Frobenius conjecture on nth roots

1-ISOMORPHISM (cf. 1-isomorphic groups): Lazard Lie group is 1-isomorphic to the additive group of its Lazard Lie ring | order statistics-equivalent not implies 1-isomorphic

Order statistics raw data

Group	Second part of GAP ID	Order 1	Order 3	Order 9	Order 27	Order 81	Order 243
Cyclic group:Z243	1	1	2	6	18	54	162
	2	1	26	216	0	0	0
	3	1	134	108	0	0	0
	4	1	80	162	0	0	0
	5	1	26	216	0	0	0
	6	1	80	162	0	0	0
	7	1	26	216	0	0	0
	8	1	26	216	0	0	0
	9	1	26	216	0	0	0
	10	1	8	72	162	0	0
	11	1	8	72	162	0	0
	12	1	26	54	162	0	0
	13	1	80	162	0	0	0
	14	1	26	216	0	0	0
	15	1	26	216	0	0	0
	16	1	26	54	162	0	0
	17	1	80	162	0	0	0
	18	1	26	216	0	0	0
	19	1	26	54	162	0	0
	20	1	26	54	162	0	0
	21	1	8	72	162	0	0
	22	1	8	72	162	0	0
	23	1	8	18	54	162	0
	24	1	8	18	54	162	0
	25	1	62	180	0	0	0
	26	1	170	72	0	0	0
	27	1	8	234	0	0	0
	28	1	116	126	0	0	0
	29	1	8	234	0	0	0
	30	1	62	180	0	0	0
	31	1	26	216	0	0	0
	32	1	80	162	0	0	0
	33	1	26	216	0	0	0
	34	1	26	216	0	0	0
	35	1	80	162	0	0	0
	36	1	26	216	0	0	0
	37	1	242	0	0	0	0
	38	1	80	162	0	0	0
	39	1	80	162	0	0	0
	40	1	80	162	0	0	0
	41	1	26	216	0	0	0
	42	1	26	216	0	0	0
	43	1	26	216	0	0	0
	44	1	26	216	0	0	0
	45	1	26	216	0	0	0
	46	1	26	216	0	0	0
	47	1	26	216	0	0	0
	48	1	26	54	162	0	0
	49	1	26	54	162	0	0
	50	1	26	54	162	0	0
	51	1	134	108	0	0	0
	52	1	80	162	0	0	0
	53	1	188	54	0	0	0
	54	1	26	216	0	0	0
	55	1	80	162	0	0	0
	56	1	134	108	0	0	0
	57	1	80	162	0	0	0
	58	1	188	54	0	0	0
	59	1	26	216	0	0	0
	60	1	80	162	0	0	0
	61	1	80	162	0	0	0
	62	1	242	0	0	0	0
	63	1	80	162	0	0	0
	64	1	80	162	0	0	0
	65	1	242	0	0	0	0
	66	1	80	162	0	0	0
Elementary abelian group:E243	1	242	0	0	0	0

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