ATLAS: Linear group L₂(97)

The following information is available for L₂(97):

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

Standard generators

Standard generators of L₂(97) are a of order 2, b of order 3 such that ab has order 97.
Standard generators of the double cover 2.L₂(97) = SL₂(97) are preimages A and B such that B has order 3 and AB has order 97.

Standard generators of L₂(97):2 = PGL₂(97) are not yet defined.
Standard generators of the double cover 2.L₂(97):2 = 2.PGL₂(97) are not yet defined.

Black box algorithms

Representations

• Some primitive permutation representations
  • Permutations on 98 points: a and b (GAP).
• Some matrix representations in characteristic 0:
  • Dimension 97 over Z: a and b (GAP).
  • Dimension 98 over Z(z48) (monomial): a and b (GAP).

• Some matrix representations in characteristic 0:
  • Dimension 98 over Z(z96) (monomial): A and B (GAP).

• none

• none

The maximal subgroups of L₂(97) are as follows.

• 97:48, with generators a, ababab²ab²ababab²abab
• D₉₈, with generators a, a^ab
• D₉₆, with generators a, a^ab2abab
• S₄, with generators a, b^ababab
• S₄, with generators a, b^{ab2ab2ababababab}

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