= Sporadic simple group
A <sporadic simple group> is one of the twenty-six exceptional <finite nonabelian simple groups> that lie outside the alternating and Lie-type families in the <classification of finite simple groups>. “Sporadic” describes their place in that classification; it does not mean randomly chosen or lacking internal structure.<Sporadic simple groups by Robert A. Wilson>[Lecture 5, introduction and Mathieu-group construction]{ref}
For example, the <Mathieu group> $M_{24}$ acts by coordinate permutations preserving the <extended binary Golay code> on twenty-four positions. Thus an exceptional <group> can emerge as the exact symmetry of a highly organized <error-correcting code>. The <Monster group> is another sporadic example, vastly larger. In contrast, the <alternating group> $A_5$ is simple but belongs to an infinite family, so is not sporadic.
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