ATLAS: Linear group L₂(233)

The following information is available for L₂(233):

• Standard generators.
• Automorphisms.
• Black box algorithms (not yet available).
• Representations.
• Maximal subgroups.

Standard generators

Standard generators of L₂(233) are a of order 2, b of order 3 such that ab has order 233.
Standard generators of the double cover 2.L₂(233) = SL₂(233) are preimages A and B such that B has order 3 and AB has order 233.

Standard generators of L₂(233):2 = PGL₂(233) are not yet defined.
Standard generators of the double cover 2.L₂(233):2 = 2.PGL₂(233) are not yet defined.

Black box algorithms

Representations

• Some primitive permutation representations
  • Permutations on 234 points: a and b (GAP).
• Some matrix representations in characteristic 0:
  • Dimension 233 over Z: a and b (GAP).
  • Dimension 234 over Z(z116) (monomial): a and b (GAP).

• Some matrix representations in characteristic 0:
  • Dimension 234 over Z(z232) (monomial): A and B (GAP).

• none

• none

The maximal subgroups of L₂(233) are as follows.

• 233:116, with generators a, ab²abab²ababab²abababab
• D₂₃₄, with generators a, a^ab2abab
• D₂₃₂, with generators a, a^ab2abababab
• S₄, with generators a, b^ab2abab2abab
• S₄, with generators a, b^{ab2ab2abab2abababab2ab}

Go to main ATLAS (version 2.0) page

Go to linear groups page