Generators and Representations for G = S₆(2)

Standard generators

• Standard generators of S₆(2) are a and b where a is in class 2A, b has order 7 and ab has order 9. (Source: ATLAS)
• Standard generators of the double cover 2.S₆(2) are preimages A and B where B has order 7 and AB has order 9. (Source: ATLAS)

BBOX programs

• Checker for S₆(2)
• CCL rep tester for S₆(2)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
S6(2)	7	+	7	χ2	Z			79%	1	0.8	perm rep on 56 points
S6(2)	15	+	15	χ3	Z			85%	1	1.5	perm rep on 72 points
S6(2)	21	+	21(a)	χ4	Z			91%	1	2.4	exterior square of χ2
			21(b)	χ5	Z			91%	3	2.4	perm rep on 56 points
S6(2)	27	+	27	χ6	Z			94%	1	3.6	perm rep on 28 points
S6(2)	35	+	35(a)	χ7	Z			80%	5	6.0	perm rep on 120 points
			35(b)	χ8	Z			95%	1	5.8	perm rep on 36 points
S6(2)	56	+	56	χ9	Z			95%	2	13.5	perm rep on 126 points
S6(2)	70	+	70	χ10	Z			87%	10	21.5	perm rep on 672a points - LLL'ed
S6(2)	84	+	84	χ11	Z			88%	6	30.3	perm rep on 120 points
S6(2)	105	+	105(a)	χ12	Z			57%	27	50.8	χ2 x χ4, rho-split, LLL'ed
			105(b)	χ13	Z			96%	1	46.3	χ2 x χ3 (corrected)
			105(c)	χ14	Z			95%	2	46.4	perm rep on 240 points
S6(2)	120	+	120	χ15	Z			86%	40	61.6	perm rep on 288 pts
S6(2)	168	+	168	χ16	Z			91%	12	118.9	perm rep on 315 pts
S6(2)	189	+	189(a)	χ17	Z			52%	132	174.2	χ2 x χ7, rho-split
			189(b)	χ18	Z			91%	32	150.2	perm rep on 576 pts
			189(c)	χ19	Z			92%	11	149.5	perm rep on 630b pts
S6(2)	210	+	210(a)	χ20	Z			90%	24	185.6	perm rep on 630c points - LLL'ed
			210(b)	χ21	Z			78%	80	196.9	perm rep on 756 points - LLL'ed
S6(2)	216	+	216	χ22	Z			91%	16	195.6	perm rep on 378 pts
2.S6(2)	8	+	No representations available
2.S6(2)	48	+	No representations available
2.S6(2)	64	o	No representations available
2.S6(2)	112	+	No representations available
2.S6(2)	120	+	No representations available
2.S6(2)	168	+	No representations available

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