Geodesic
On the prime graphs of the automorphism groups of sporadic simple groups
Archivum mathematicum, Tome 45 (2009) no. 2, pp. 83-94.

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In this paper as the main result, we determine finite groups with the same prime graph as the automorphism group of a sporadic simple group, except $J_2$.
Classification : 05C25, 20D05, 20D08, 20D45, 20D60
Keywords: automorphism group of a sporadic simple group; prime graph 
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Khosravi, Behrooz. On the prime graphs of the automorphism groups of sporadic simple groups. Archivum mathematicum, Tome 45 (2009) no. 2, pp. 83-94. http://geodesic.mathdoc.fr/item/ARM_2009__45_2_a1/