Sporadic simple group

A simple finite group that does not belong to any of the known infinite series of simple finite groups. The twenty-six sporadic simple groups are listed in the following table.'

<tbody> </tbody> notation name order Mathieu groups Janko group , Hall–Janko group , Higman–Janko–McKay group Janko group , , Conway groups , , , Fischer groups , Higman–Sims group , Held–Higman–McKay group Suzuki group McLaughlin group Lyons group Rudvalis group , O'Nan–Sims group , Monster, Fischer–Griess group , Baby monster , , Thompson group , , Harada–Norton group

References

[1]	S.A. Syskin, "Abstract properties of the simple sporadic groups" Russian Math. Surveys , 35 : 5 (1980) pp. 209–246 Uspekhi Mat. Nauk , 35 : 5 (1980) pp. 181–212
[2]	M. Aschbacher, "The finite simple groups and their classification" , Yale Univ. Press (1980)

Comments

The recent classification of the finite simple groups (1981) has led to the conclusion that — up to a uniqueness proof for the Monster as the only simple group of its order with certain additional properties — every non-Abelian finite simple group is isomorphic to: an alternating group on at least letters, a group of (twisted or untwisted) Lie type, or one of the above sporadic groups. See [a2] for a discussion of the proof.

References

[a1]	J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, R.A. Wilson, "Atlas of finite groups" , Clarendon Press (1985)
[a2]	D. Gorenstein, "Finite simple groups. An introduction to their classification" , Plenum (1982)