Maximal subgroups of the Coxeter group W(H4) and quaternions

Mehmet Koca, Ramazan Koç, Muataz Al Barwani, Shadia Al-Farsi

Research output: Contribution to journalArticlepeer-review


The largest finite subgroup of O(4) is the non-crystallographic Coxeter group W(H4) of order 14,400. Its derived subgroup is the largest finite subgroup W(H4)/Z2 of SO(4) of order 7200. Moreover, up to conjugacy, it has five non-normal maximal subgroups of orders 144, two 240, 400 and 576. Two groups [W(H2) × W(H2)]⋊ Z4 and W(H3) × Z2 possess non-crystallographic structures with orders 400 and 240 respectively. The groups of orders 144, 240 and 576 are the extensions of the Weyl groups of the root systems of SU(3) × SU(3), SU(5) and SO(8) respectively. We represent the maximal subgroups of W(H4) with sets of quaternion pairs acting on the quaternionic root systems.

Original languageEnglish (US)
Pages (from-to)441-452
Number of pages12
JournalLinear Algebra and Its Applications
Issue number2-3
StatePublished - Jan 15 2006
Externally publishedYes


  • Coxeter groups
  • Quaternions
  • Structure of groups
  • Subgroup structure

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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