ATLAS: Linear group L₂(97)

Order = 456288 = 2⁵.3.7².97.
Mult = 2.
Out = 2.

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Porting notes

Porting incomplete.

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Standard generators

Standard generators of L₂(97) are a, b where a has order 2, b has order 3 and ab has order 97.

Standard generators of 2.L₂(97) are preimages A, B where B has order 3 and AB has order 97.

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Representations

Representations of L₂(97)

• View detailed report.
• Permutation representations:

  Number of points	ID	Generators	Description	Link
  98		Std		Details

• Matrix representations

  Char	Ring	Dimension	ID	Generators	Description	Link
  0	Z	97		Std		Details
  0	Z[z48]	98	a	Std		Details

Representations of 2.L₂(97)

• View detailed report.
• Matrix representations

  Char	Ring	Dimension	ID	Generators	Description	Link
  0	Z[z96]	98	a	Std		Details

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Maximal subgroups

Maximal subgroups of L₂(97)

Subgroup	Order	Index	Programs/reps
97:48			Program: Generators
D98			Program: Generators
D96			Program: Generators
S4			Program: Generators
S4			Program: Generators

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Standard generators
Representations
Maximal subgroups

Groups

L₂(97)
2.L₂(97)
L₂(97):2
2.L₂(97):2