[seqfan] Subquotients of sporadic simple groups

Charles Greathouse charles.greathouse at case.edu
Thu Sep 17 20:24:13 CEST 2015

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
Case Western Reserve University

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