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A sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. All the other finite simple groups form 18 infinite families numbered by q - power of prime number and n - natural number. Sporadic groups attach attention due to their sporadic/exceptional nature - similar to exceptional Lie groups. The first sporadic groups were found by Mathieu in 1860s. The last sporadic group J4 was discovered in 1975 by Janko.

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Fixed points of the automorphisms of sporadic groups

I think the information you are looking for is in Table~5.3 of GLS3: Gorenstein, Daniel; Lyons, Richard; Solomon, Ronald. The classification of the finite simple groups. Number 3. Part I. Cha …
Justin Lynd's user avatar