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.

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

Author

Sven Simon and Charles R Greathouse IV, Oct 18 2015

Keywords

• nonn
• fini
• full

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.

Links

• Wikipedia, Sporadic group

Crossrefs

Cf. A001228, A261717 (another version).

Extensions

Terms confirmed by N. J. A. Sloane, Oct 19 2015