ATLAS: Linear group L₂(239)

Order = 6825840 = 2⁴.3.5.7.17.239.
Mult = 2.
Out = 2.

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Porting notes

Porting incomplete.

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Standard generators

Standard generators of L₂(239) are a, b where a has order 2, b has order 3 and ab has order 239.

Standard generators of 2.L₂(239) are preimages A, B where B has order 3 and AB has order 239.

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Representations

Representations of L₂(239)

• View detailed report.
• Permutation representations:

  Number of points	ID	Generators	Description	Link
  240		Std		Details

• Matrix representations

  Char	Ring	Dimension	ID	Generators	Description	Link
  0	Z	239		Std		Details
  0	Z[z119]	240	a	Std		Details

Representations of 2.L₂(239)

• View detailed report.
• Matrix representations

  Char	Ring	Dimension	ID	Generators	Description	Link
  0	Z[z238]	240	a	Std		Details

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Maximal subgroups

Maximal subgroups of L₂(239)

Subgroup	Order	Index	Programs/reps
239:119			Program: Generators
D240			Program: Generators
D238			Program: Generators
A5			Program: Generators
A5			Program: Generators
S4			Program: Generators
S4			Program: Generators

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Standard generators
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L₂(239)
2.L₂(239)
L₂(239):2
2.L₂(239):2