---
tag: ZYZ5FYG7QC
kind: concept
name: Pariah groups
msc: [20D08]
specializes: [PZ49Z4CBFZ]
sources:
  - url: https://en.wikipedia.org/wiki/Pariah_group
same_as:
  wikidata: Q278338
  wikipedia: Pariah group
---

## Summary

The pariah groups are the six sporadic simple groups that are not subquotients of the Monster group.
They are the Janko groups $J_1$, $J_3$ and $J_4$, the O'Nan group, the Rudvalis group and the Lyons group.
The other twenty sporadic groups, which are subquotients of the Monster, form the happy family; the name pariah is due to Robert Griess.

## Explanations

### L1 human

The Monster group contains, as pieces of its subgroups, most of the exceptional finite simple groups.
Six exceptional groups do not fit inside it in this way.
They stand apart from the rest, so they are called the pariahs.