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A263447
Arrange the 26 sporadic simple groups in increasing order; a(n) = number of sporadic simple groups which are subquotients of the n-th largest sporadic simple group.
2
1, 2, 1, 1, 1, 3, 3, 1, 5, 3, 1, 1, 4, 3, 7, 6, 4, 5, 4, 1, 6, 12, 6, 9, 12, 20
OFFSET
1,2
COMMENTS
A group is a subquotient of itself, so a(n) >= 1.
It is well-known that a(26) = 20, the so-called "happy family". Trivially a(1) = 1 and a(2) = 2 since M_11 is a subquotient of M_12.
The sequence was generated from the diagram of subquotient relations on page 238 of the ATLAS, together with the update that J_1 is not involved in M (which replaces the single question mark in the table with a plus sign).
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 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites]. See page 238.
CROSSREFS
Cf. A001228, A261717 (another version).
Sequence in context: A344911 A321915 A321748 * A180303 A118923 A292745
KEYWORD
nonn,fini,full
AUTHOR
EXTENSIONS
Terms confirmed by N. J. A. Sloane, Oct 19 2015
STATUS
approved