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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.
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%I #20 Jun 14 2024 22:31:10

%S 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

%N 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.

%C A group is a subquotient of itself, so a(n) >= 1.

%C 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.

%C 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).

%D 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.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sporadic_group">Sporadic group</a>

%Y Cf. A001228, A261717 (another version).

%K nonn,fini,full

%O 1,2

%A _Sven Simon_ and _Charles R Greathouse IV_, Oct 18 2015

%E Terms confirmed by _N. J. A. Sloane_, Oct 19 2015