Largest simple groups with fully factorized order

A by-product of the is the full factorization of the orders of many Lie groups based on a power of a small prime.
== Records ==
s will not be listed here.
Family 	Parameter 	Year found	Number of digits in the order
s Cn 	n = 277,232,917 − 1 	2018 	23,249,425
s An 	n is somewhere between a million and a googol 	– 	–
s L2(n) 	n = 2,618,163,402,417 × 21,290,001 − 1 	2016 	1,165,024
s Ln(2) 	n = 1,206https://homes.cerias.purdue.edu/~ssw/cun/champ 	– 	437,829
s Ln(3) 	n = 660 	– 	207,834
s Ln(4) 	n = 1,032 	– 	641,208
s Ln(5) 	n = 448 	– 	140,285
s Ln(7) 	n = 358 	– 	108,310
s Ln(8) 	n = 436Jonathan Crombie Future Cunningham Extensions 2011-12-02. Archived 2022-12-16.	– 	170,101
s Ln(9) 	n = 646 	– 	398,220
s Ln(11) 	n = 292 	– 	88,792
s Ln(13) 	n = 208http://maths-people.anu.edu.au/~brent/ftp/factors/holes.txt 	– 	48,192
s Ln(16) 	n = 525 	– 	331,884
Sz(22n+1) 	n ≥ 742 	– 	2,236
2F4(22n+1)	n ≥ 247 	– 	3,875
R(32n+1) 	n ≥ 282Factorizations of 2^n-1, n odd, n<1300 Archived 2017-11-24. 	– 	1,888
== Sources ==
Category:Numbers
Category:Class 2
Category:Numbers with 1000 to 1000000 digits
Category:Numerical records
Category:Orders of non-abelian simple groups
Category:Dynamic googolisms