Representation of the 26 sporadic groups

Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks (Part #7)

---

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]

---

One way of representing the sporadic groups is in terms of their constituent prime number factors -- as indicated above for the Monster group. They could then be presented as in Table 1.

Table 1: Sporadic group prime number factors (and powers) Cells of table contain factor powers (e.g. 3N) Shaded rows indicate those groups that are not subgroups of the Monster group Note that the groups together use primes in the first 20 prime numbers, excepting 53 and 61
Sporadic group		Prime factors											Order / Size
.	.	2	3	5	7	11	13	17	19	23	Other factors	Total	.
Mathieu	M24	10	3	1	1	1	.	.	.	1	.	17	244823040
	M23	7	2	1	1	1	.	.	.	1	.	13	10200960
	M22	7	2	1	1	1	.	.	.	.	.	12	443520
	M12	6	3	1	.	1	.	.	.	.	.	11	95040
	M11	4	2	1	.	1	.	.	.	.	.	8	7920
Janko	J1	3	1	1	1	.	.	.	1	.	.	7	175560
	J2	7	3	2	1	.	.	.	.	.	.	13	604800
	J3	7	5	1	.	.	.	1	1	.	.	15	50232960
	J4	21	3	1	1	3	.	.	.	1	29, 31, 37, 43	34	86775571046077562880
Higman-Sims	HS	9	2	3	1	1	.	.	.	.	.	16	44352000
McLaughlin	Mc	7	6	3	1	1	.	.	.	.	.	18	898128000
Held	He	10	3	2	3	.	.	1	.	.	.	19	4030387200
Suzuki	Suz	13	7	2	1	1	1	.	.	.	.	25	448345497600
Rudvalis	Ru	14	3	3	1	.	1	.	.	.	29	23	145926144000
O'Nan	ON	9	4	1	3	1	.	.	1	.	31	20	460815505920
Lyons	Ly	8	7	6	1	1	.	.	.	.	31, 37, 67	26	51765179004000000
Conway	Co1	21	9	4	2	1	1	.	.	1	.	39	4157776806543360000
	Co2	18	6	3	1	1	.	.	.	1	.	30	42305421312000
	Co3	10	7	3	1	1	.	.	.	1	.	23	495766656000
Fischer	Fi22	17	9	2	1	1	1.	.	.	.	.	31	64561751654400
	Fi23	18	13	2	1	1	1	1	.	1	.	38	4089470473293004800
	Fi24	21	16	2	3	1	1	1	.	1	29	48	1255205709190661721292800
Harada-Norton	HN	14	6	6	1	1	.	.	1	.	.	29	273030912000000
Thompson	Th	15	10	3	2	.	1	.	1	.	31	33	90745943887872000
Baby Monster	B	41	13	6	2	1	1	1	1	1	31, 47	69	4154781481226426191177580544000000
Monster	M	46	20	9	6	2	3	1	1	1	29, 31, 41, 47, 59, 71	95	808017424794512875886459904961710 757005754368000000000
Total	.	363	165	70	37	23	11	7	7	10	19	712	.

---

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]