# [seqfan] Re: Subquotients of sporadic simple groups

Sven Simon sven-h.simon at gmx.de
Sun Sep 20 22:29:40 CEST 2015

As the idea of Charles was interesting, I calculated the values by hand - but they were double checked, so I am sure, they are correct.
The sequence is
1,2,1,2,1,3,3,1,5,5,2,2,5,5,9,9,6,8,6,2,9,13,6,11,19,20

I will add the sequence to the OEIS, using the description of Charles.
Sven

-----Ursprüngliche Nachricht-----
Von: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] Im Auftrag von Charles Greathouse
Gesendet: Donnerstag, 17. September 2015 20:24
An: Sequence Fanatics Discussion list
Betreff: [seqfan] Subquotients of sporadic simple groups

Arrange the sporadic simple groups by increasing order 1, 2, ..., 26, then define a(n) = Number of sporadic simple groups which are subquotients of the n-th largest sporadic simple group.

I don't think this sequence is in the OEIS, and it seems interesting. Are all these terms known? Can this sequence be added to the OEIS?

It's well-known that a(26) = 20, the so-called "happy family". Trivially
a(1) = 1 and a(2) = 2 since M11 is a subquotient of M12 (and itself). a(3) = 1 since the Janko group J1 has order 2^3 * ... and 2^4 divides the orders of M11 and M12.

I've seen diagrams giving (the transitive reduction of) the subquotient relationships, but I don't know if they're known to be complete. If not, what's the smallest group with an open question?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

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