ATLAS: Linear group L₂(181)

The following information is available for L₂(181):

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

Standard generators

Standard generators of L₂(181) are a of order 2, b of order 3 such that ab has order 181.
Standard generators of the double cover 2.L₂(181) = SL₂(181) are preimages A and B such that B has order 3 and AB has order 181.

Standard generators of L₂(181):2 = PGL₂(181) are not yet defined.
Standard generators of the double cover 2.L₂(181):2 = 2.PGL₂(181) are not yet defined.

Black box algorithms

Representations

• Some primitive permutation representations
  • Permutations on 182 points: a and b (GAP).
• Some matrix representations in characteristic 0:
  • Dimension 181 over Z: a and b (GAP).
  • Dimension 182 over Z(z90) (monomial): a and b (GAP).

• Some matrix representations in characteristic 0:
  • Dimension 182 over Z(z180) (monomial): A and B (GAP).

• none

• none

The maximal subgroups of L₂(181) are as follows.

• 181:90, with generators a, ab²abababababab²ab²ab
• D₁₈₂, with generators a, a^abab
• D₁₈₀, with generators a, a^abab2ababab
• A₅, with standard generators a, b^ababab
• A₅, with standard generators a, b^{ababab2ababab}

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