Generators and Representations for G = S₆(3)

Standard generators

• Standard generators of S6(3) are a and b where a is in class 2A, b has order 5, ab has order 13 and abb has order 14. (Source: ATLAS)
• Standard generators of the double cover 2.S6(3) are preimages A and B where B has order 5 and AB has order 13. (Source: ATLAS)

BBOX programs

• Checker for S₆(3)
• CCL rep tester for S₆(3)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
S6(3)	13	o	13(a)	χ2	Z(ω)			80%		1.3	complex conjugate
			13(b)	χ3	Z(ω)			80%		1.3	Weil rep
S6(3)	78	+	78	χ4	Z(ω)			93%		26.7	exterior square of χ2
S6(3)	91	o	91(a)	χ5	Z(ω)			93%		36.3	symmetric square of χ2
			91(b)	χ6	Z(ω)			93%		36.3	complex conjugate
S6(3)	105	+	105	χ7	Z			89%	10	47.1	perm rep on 1120 pts
S6(3)	168	+	168	χ8	Z			95%	7	117.8	perm rep on 364 pts
S6(3)	195	+	195	χ9	Z			89%	22	161.2	perm rep on 364 pts
2.S6(3)	14	o	No representations available
2.S6(3)	182	-	No representations available
2.S6(3)	182	o	No representations available

Notes

Element xyxy²xy³ is assumed to be in class 36A.

Last generated on Sat Sep 24 18:53:21 2005