ATLAS: Symplectic group S₄(9)

Order = 1721606400 = 2⁸.3⁸.5².41.
Mult = 2.
Out = 2².

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Porting notes

Fully copied from version 2. 29/7/06.

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Standard generators

Standard generators of S₄(9) are a, b where a is in class 2B, b is in class 4B, ab has order 41 and ababbb has order 5.

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Black box algorithms

Checking generators (semi-presentations)

Group	Semi-presentation	File
S4(9)	〈〈 a, b | some conditions 〉〉	Download

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Representations

Representations of 2.S₄(9)

• View detailed report.
• Matrix representations

  Char	Ring	Dimension	ID	Generators	Description	Link
  3	GF(9)	4				Details

Representations of S₄(9)

• View detailed report.
• Permutation representations:

  Number of points	ID	Generators	Description	Link
  820	a	Std		Details
  820	b	Std		Details
  1640		Std		Details

• Matrix representations

  Char	Ring	Dimension	ID	Generators	Description	Link
  0	Z	41	a	Std		Details
  0	Z	41	b	Std		Details

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2.S₄(9)
S₄(9)