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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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How many sporadic simple groups are there, really?
I attended a talk by John Conway recently where he explained to us that the usual number, 26, was wrong, that there are in fact 27 sporadic simple groups. His reason was that the Tits group, which is …