ATLAS: Linear group L₂(157)

Order = 1934868 = 2².3.13.79.157.
Mult = 2.
Out = 2.

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Porting notes

Porting incomplete.

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Standard generators

Standard generators of L₂(157) are a, b where a has order 2, b has order 3 and ab has order 157.

Standard generators of 2.L₂(157) are preimages A, B where B has order 3 and AB has order 157.

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Representations

Representations of L₂(157)

• View detailed report.
• Permutation representations:

  Number of points	ID	Generators	Description	Link
  158		Std		Details

• Matrix representations

  Char	Ring	Dimension	ID	Generators	Description	Link
  0	Z	157		Std		Details
  0	Z[z78]	158	a	Std		Details

Representations of 2.L₂(157)

• View detailed report.
• Matrix representations

  Char	Ring	Dimension	ID	Generators	Description	Link
  0	Z[z156]	158	a	Std		Details

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Maximal subgroups

Maximal subgroups of L₂(157)

Subgroup	Order	Index	Programs/reps
157:78			Program: Generators
D158			Program: Generators
D156			Program: Generators
A4			Program: Generators

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Standard generators
Representations
Maximal subgroups

Groups

L₂(157)
2.L₂(157)
L₂(157):2
2.L₂(157):2