cp's OEIS Frontend

A353341 Number of 4-dimensional point groups of order n.

%I A353341 #34 May 16 2022 10:02:40
%S A353341 1,4,3,11,4,14,5,29,8,18,7,41,8,22,14,56,10,37,11,51,18,30,13,100,17,
%T A353341 34,22,60,16,64,17,98,26,42,26,101,20,46,30,112,22,80,23,80,42,54,25,
%U A353341 189,30,73,38,91,28,96,38,133,42,66,31,170,32,70,55,167,44
%N A353341 Number of 4-dimensional point groups of order n.
%C A353341 In other words, the number of (finite) subgroups of order n of the orthogonal group O(4).
%D A353341 John H. Conway and Derek A. Smith, On Quaternions and Octonions, CRC Press, 2003.
%D A353341 Patrick Du Val, Homographies, Quaternions and Rotations. Clarendon Press, 1964.
%H A353341 Laith Rastanawi and Günter Rote, <a href="/A353341/b353341.txt">Table of n, a(n) for n = 1..10000</a>
%H A353341 Edouard Goursat, <a href="https://doi.org/10.24033/asens.317">Sur les substitutions orthogonales et les divisions régulières de l'espace</a>, Annales scientifiques de l'E.N.S. 3e série, 6:9-102, 1889.
%H A353341 A. C. Hurley, <a href="https://doi.org/10.1017/S0305004100027109">Finite rotation groups and crystal classes in four dimensions</a>, Mathematical Proceedings of the Cambridge Philosophical Society, 47(4):650-661, 1951.
%H A353341 Laith Rastanawi and Günter Rote, <a href="https://arxiv.org/abs/2205.04965">Towards a Geometric Understanding of the 4-Dimensional Point Groups</a>, arXiv preprint arXiv:2205.04965 [math.MG], 2022.
%H A353341 Laith Rastanawi and Günter Rote, <a href="https://github.com/LaisRast/point-groups/blob/main/generate_oeis_sequences.sage">Sage code used to generate the sequence</a>.
%H A353341 W. Threlfall and H. Seifert, <a href="https://doi.org/10.1007/BF01457920">Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes</a>, Math. Annalen, 104:1-70, 1931.
%H A353341 W. Threlfall and H. Seifert, <a href="https://doi.org/10.1007/BF01448910">Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes (Schluß)</a>, Math. Annalen, 107:543-586, 1933.
%Y A353341 Cf. A354046.
%K A353341 nonn
%O A353341 1,2
%A A353341 _Laith Rastanawi_ and _Günter Rote_, May 16 2022