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A353341 Number of 4-dimensional point groups of order n. 2
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, 34, 22, 60, 16, 64, 17, 98, 26, 42, 26, 101, 20, 46, 30, 112, 22, 80, 23, 80, 42, 54, 25, 189, 30, 73, 38, 91, 28, 96, 38, 133, 42, 66, 31, 170, 32, 70, 55, 167, 44 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
In other words, the number of (finite) subgroups of order n of the orthogonal group O(4).
REFERENCES
John H. Conway and Derek A. Smith, On Quaternions and Octonions, CRC Press, 2003.
Patrick Du Val, Homographies, Quaternions and Rotations. Clarendon Press, 1964.
LINKS
Laith Rastanawi and Günter Rote, Table of n, a(n) for n = 1..10000
Edouard Goursat, Sur les substitutions orthogonales et les divisions régulières de l'espace, Annales scientifiques de l'E.N.S. 3e série, 6:9-102, 1889.
A. C. Hurley, Finite rotation groups and crystal classes in four dimensions, Mathematical Proceedings of the Cambridge Philosophical Society, 47(4):650-661, 1951.
Laith Rastanawi and Günter Rote, Towards a Geometric Understanding of the 4-Dimensional Point Groups, arXiv preprint arXiv:2205.04965 [math.MG], 2022.
Laith Rastanawi and Günter Rote, Sage code used to generate the sequence.
CROSSREFS
Cf. A354046.
Sequence in context: A222510 A100492 A072183 * A346614 A370631 A370630
KEYWORD
nonn
AUTHOR
Laith Rastanawi and Günter Rote, May 16 2022
STATUS
approved

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Last modified July 19 03:15 EDT 2024. Contains 374388 sequences. (Running on oeis4.)