Non-isomorphic simple groups may have the same order

This fact is related to: group theory
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Statement

Two non-isomorphic simple groups may have the same order.

Proof

By example

The groups alternating group:A8 and projective special linear group:PSL(3,4) are non-isomorphic, and are both groups of order 20160. The fact that these are non-isomorphic can be shown by various means. For example, the former has 14 conjugacy classes, the latter has 10.

History

This was first proven by Ida May Schottenfels, giving the example of alternating group:A8 and projective special linear group:PSL(3,4).

See also

It turns out that if there is more than one simple group of a certain order, then there are exactly two, see there are at most two finite simple groups of any order.

External links

See Oeis:A119648 for the list of numbers for which there are two non-isomorphic simple groups of said order.