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A330585
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The orders, with repetition, of the non-cyclic finite simple groups that are subquotients of the sporadic finite simple groups.
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2
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60, 168, 360, 504, 660, 1092, 2448, 2520, 3420, 4080, 5616, 6048, 6072, 7800, 7920, 12180, 14880, 20160, 20160, 25920, 29120, 32736, 58800, 62400, 95040, 102660, 126000, 175560, 178920, 181440, 265680, 372000, 443520, 604800
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OFFSET
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1,1
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COMMENTS
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By the classification theorem for finite simple groups, there are exactly 26 sporadic finite simple groups, whose orders form A001228. The online ATLAS includes lists of the maximal subgroups of these groups, and entries for their simple subquotients.
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REFERENCES
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J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985.
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LINKS
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EXAMPLE
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This list includes the orders of all non-cyclic simple groups of order less than 9828. L2(27), of order 9828, does not appear as a subquotient of any of the sporadic finite simple groups.
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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