Generators and Representations for G = S₆(5)

Standard generators

• Standard generators of S₆(5) are a and b where a is in class 2A, b is in class 8A, ab has order 9 and abababbabb has order 15. (Source: thesis)
• Standard generators of the double cover 2.S₆(5) = Sp₆(5) are preimages A and B such that AB has order 9 and ABB has order 31. (NOTE: extra condition added 7/2/05). (Source: thesis)

BBOX programs

• Finder for S₆(5)
• Checker for S₆(5)
• CCL rep tester for S₆(5)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
S6(5)	63	+	63(a)	χ2	C			64%		41.8	Weil rep.
			63(b)	χ3	C			64%		41.8	Galois conjugate of χ2
2.S6(5)	62	-	No representations available

Notes

The Hiss-Malle list appears to have the representations for S₆(5) and 2.S₆(5) the wrong way round. We have made the necessary changes in our list.

We assume the element (xy³xy²xy)³ is in class 40A rather than 40B.

Last generated on Sat Sep 24 18:53:22 2005