

A330585


The orders, with repetition, of the noncyclic finite simple groups that are subquotients of the sporadic finite simple groups.


2



60, 168, 360, 504, 660, 1092, 2448, 2520, 3420, 4080, 5616, 6048, 6072, 7800, 7920, 12180, 14880, 20160, 20160, 25920, 29120, 32736, 58800, 62400, 95040, 102660, 126000, 175560, 178920, 181440, 265680, 372000, 443520, 604800
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OFFSET

1,1


COMMENTS

By the classification theorem for finite simple groups, there are exactly 26 sporadic finite simple groups, whose orders form A001228. The online ATLAS includes lists of the maximal subgroups of these groups, and entries for their simple subquotients.
Subsequence of A083207.  Ivan N. Ianakiev, Jan 02 2020


REFERENCES

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985.


LINKS

Hal M. Switkay, Table of n, a(n) for n = 1..82
Ivan N. Ianakiev, Subsequence of A083207, Proof
David A. Madore, Orders of nonabelian simple groups
R. A. Wilson et al., ATLAS of Finite Group Representations  Version 3


EXAMPLE

This list includes the orders of all noncyclic simple groups of order less than 9828. L2(27), of order 9828, does not appear as a subquotient of any of the sporadic finite simple groups.


CROSSREFS

Cf. A109379, A001228, A083207.
Sequence in context: A109379 A001034 A330583 * A330584 A330586 A119630
Adjacent sequences: A330582 A330583 A330584 * A330586 A330587 A330588


KEYWORD

nonn,fini,full


AUTHOR

Hal M. Switkay, Dec 18 2019


STATUS

approved



