ATLAS: Linear group L₂(241)

The following information is available for L₂(241):

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

Standard generators

Standard generators of L₂(241) are a of order 2, b of order 3 such that ab has order 241.
Standard generators of the double cover 2.L₂(241) = SL₂(241) are preimages A and B such that B has order 3 and AB has order 241.

Standard generators of L₂(241):2 = PGL₂(241) are not yet defined.
Standard generators of the double cover 2.L₂(241):2 = 2.PGL₂(241) are not yet defined.

Black box algorithms

Representations

• Some primitive permutation representations
  • Permutations on 242 points: a and b (GAP).
• Some matrix representations in characteristic 0:
  • Dimension 241 over Z: a and b (GAP).
  • Dimension 242 over Z(z120) (monomial): a and b (GAP).

• Some matrix representations in characteristic 0:
  • Dimension 242 over Z(z240) (monomial): A and B (GAP).

• none

• none

The maximal subgroups of L₂(241) are as follows.

• 241:120, with generators a, ab²abababab²abab²abab²abababab
• D₂₄₂, with generators a, a^ababab
• D₂₄₀, with generators a, a^{abab2ab2ab2abab}
• A₅, with standard generators a, b^ababab2ab
• A₅, with standard generators a, b^{ab2ab2ab2ab2ab}
• S₄, with generators a, b^ab2abab
• S₄, with generators a, b^abababab

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