ATLAS: Linear group L₂(151)

The following information is available for L₂(151):

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

Standard generators

Standard generators of L₂(151) are a of order 2, b of order 3 such that ab has order 151.
Standard generators of the double cover 2.L₂(151) = SL₂(151) are preimages A and B such that B has order 3 and AB has order 151.

Standard generators of L₂(151):2 = PGL₂(151) are not yet defined.
Standard generators of the double cover 2.L₂(151):2 = 2.PGL₂(151) are not yet defined.

Black box algorithms

Representations

• Some primitive permutation representations
  • Permutations on 152 points: a and b (GAP).
• Some matrix representations in characteristic 0:
  • Dimension 151 over Z: a and b (GAP).
  • Dimension 152 over Z(z75) (monomial): a and b (GAP).

• Some matrix representations in characteristic 0:
  • Dimension 152 over Z(z150) (monomial): A and B (GAP).

• none

• none

The maximal subgroups of L₂(151) are as follows.

• 151:75, with generators ab², abab²ababab²ab²ab²ababab²abab
• D₁₅₂, with generators a, a^ababab
• D₁₅₀, with generators a, a^abab
• A₅, with standard generators a, b^abab2abab2ab
• A₅, with standard generators a, b^{ab2abab2abab2}
• S₄, with generators a, b^ab2ab2abab
• S₄, with generators a, b^ababab2ab2

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