ATLAS: Linear group L₂(197)

The following information is available for L₂(197):

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

Standard generators

Standard generators of L₂(197) are a of order 2, b of order 3 such that ab has order 197.
Standard generators of the double cover 2.L₂(197) = SL₂(197) are preimages A and B such that B has order 3 and AB has order 197.

Standard generators of L₂(197):2 = PGL₂(197) are not yet defined.
Standard generators of the double cover 2.L₂(197):2 = 2.PGL₂(197) are not yet defined.

Black box algorithms

Representations

• Some primitive permutation representations
  • Permutations on 198 points: a and b (GAP).
• Some matrix representations in characteristic 0:
  • Dimension 197 over Z: a and b (GAP).
  • Dimension 198 over Z(z98) (monomial): a and b (GAP).

• Some matrix representations in characteristic 0:
  • Dimension 198 over Z(z196) (monomial): A and B (GAP).

• none

• none

The maximal subgroups of L₂(197) are as follows.

• 197:98, with generators a, abab²ab²ab²ababab²ababab
• D₁₉₈, with generators a, a^ab
• D₁₉₆, with generators a, a^ab2abab
• A₄, with generators a, b^{ab2abababab2ab2ab}

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