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Search: id:A046057
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| A046057 |
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Smallest order for which there are n nonisomorphic finite groups, or 0 if no such order exists. |
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+0
4
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| 1, 4, 75, 28, 8, 42, 375, 510, 308, 90, 140, 88, 56, 16, 24, 100, 675, 156, 1029, 820, 1875, 6321, 294, 546, 2450, 2550, 1210, 2156, 1380, 270
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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R. Keith Dennis conjectures that there are no 0's in this sequence. See A053403 for details.
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REFERENCES
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H.-U. Besche and B. Eick, Construction of Finite Groups, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 387-404.
H.-U. Besche and B. Eick, The Groups of Order at Most 1000 Except 512 and 768, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 405-413.
J. H. Conway et al., The Symmetries of Things, Peters, 2008, p. 209.
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LINKS
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H.-U. Besche, The Small Groups library
John H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica.
John H. Conway, Heiko Dietrich and E. A. O'Brien, Table of n, a(n) for n = 1..100 (with some question marks)
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for groups
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CROSSREFS
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Cf. A000001, A046056, A046058, A046059, A053403.
Adjacent sequences: A046054 A046055 A046056 this_sequence A046058 A046059 A046060
Sequence in context: A100865 A007157 A000857 this_sequence A072373 A006412 A137220
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KEYWORD
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nonn,more,new
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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More terms from Victoria A. Sapko (vsapko(AT)canes.gsw.edu), Nov 04 2003
a(20) corrected Jan 21, 2004.
More terms from njas Oct 03 2008, from the John H. Conway, Heiko Dietrich and E. A. O'Brien article.
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