ATLAS: Linear group L₂(163)

Order = 2165292 = 2².3⁴.41.163.
Mult = 2.
Out = 2.

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Porting notes

Porting incomplete.

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Standard generators

Standard generators of L₂(163) are a, b where a has order 2, b has order 3 and ab has order 163.

Standard generators of 2.L₂(163) are preimages A, B where B has order 3 and AB has order 163.

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Representations

Representations of L₂(163)

• View detailed report.
• Permutation representations:

  Number of points	ID	Generators	Description	Link
  164		Std		Details

• Matrix representations

  Char	Ring	Dimension	ID	Generators	Description	Link
  0	Z	163		Std		Details
  0	Z[z81]	164	a	Std		Details

Representations of 2.L₂(163)

• View detailed report.
• Matrix representations

  Char	Ring	Dimension	ID	Generators	Description	Link
  0	Z[z162]	164	a	Std		Details

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Maximal subgroups

Maximal subgroups of L₂(163)

Subgroup	Order	Index	Programs/reps
163:81			Program: Generators
D164			Program: Generators
D162			Program: Generators
A4			Program: Generators

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Standard generators
Representations
Maximal subgroups

Groups

L₂(163)
2.L₂(163)
L₂(163):2
2.L₂(163):2