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Search: id:A064527
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| A064527 |
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Numbers n such that there exists a finite group G such that all entries in its character table are integers. |
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+0
1
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| 1, 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 54, 64, 72, 96, 108, 120, 128, 144, 162, 192, 200, 216, 240, 256, 288, 324, 384, 400
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The list contains all numbers of the form 2^w*3^u for w> 0, u>=0. But it also contains 120, 200, 240 and 400. It contains n! for all n because the symmetric groups have integral character tables. By taking direct products, we get all numbers of the form n! * 2^w * 3^u, w >= 0, u >= 0. The 200 comes from a semidirect product of an elementary group of order 25 with a quaternion group of order 8, with fixed-point-free action (a Frobenius group). - Derek Holt
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CROSSREFS
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Contains A000142 and A007694.
Sequence in context: A140067 A067946 A145853 this_sequence A007694 A050622 A082662
Adjacent sequences: A064524 A064525 A064526 this_sequence A064528 A064529 A064530
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KEYWORD
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nonn,nice
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AUTHOR
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Tim Brooks (tim_brooks(AT)my-deja.com), Oct 07 2001
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EXTENSIONS
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More terms from Derek Holt (mareg(AT)csv.warwick.ac.uk), Oct 07, 2001
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