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A066085
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Orders of non-supersolvable groups.
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5
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12, 24, 36, 48, 56, 60, 72, 75, 80, 84, 96, 108, 112, 120, 132, 144, 150, 156, 160, 168, 180, 192, 196, 200, 204, 216, 224, 225, 228, 240, 252, 264, 276, 280, 288, 294, 300, 312, 320, 324, 336, 348, 351, 360, 363, 372, 375, 384, 392, 396, 400, 405, 408, 420
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OFFSET
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1,1
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COMMENTS
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A finite group is supersolvable if it has a normal series with cyclic factors. Huppert showed that a finite group is supersolvable iff the index of any maximal subgroup is prime.
All multiples of non-supersolvable orders are non-supersolvable orders. - Des MacHale, Dec 22 2003
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LINKS
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EXAMPLE
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a(1)=12 is in the sequence since the alternating group on 4 elements is the smallest group which is not supersolvable.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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