Generators and Representations for G = S₄(7)

Standard generators

• Standard generators of S₄(7) are a and b where a is in class 2A, b has order 5 and ab has order 7. (Source: ATLAS)
• Standard generators of the double cover 2.S₄(7) = Sp₄(7) are preimages A and B where B has order 5 and AB has order 7. (Source: ATLAS)

BBOX programs

• Checker for S₄(7)
• CCL rep tester for S₄(7)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
S4(7)	25	o	25(a)	χ2	C			78%		3.8	perm rep on 800 points, algebraic integers
			25(b)	χ3	C			78%		3.8	complex conjugate of χ2
S4(7)	126	+	126	χ4	Z			73%	45	70.7	perm rep on 2352 points, LLL'ed
S4(7)	150	o	No representations available
S4(7)	175	+	175(a)	χ7	Z			92%	8	128.4	perm rep on 400a points
			175(b)	χ8	Z			80%	73	134.4	perm rep on 400b points, LLL'ed
S4(7)	224	+	224	χ9	Z			93%	8	209.1	perm rep on 400a points
2.S4(7)	24	o	No representations available
2.S4(7)	200	o	No representations available

Notes

We assume xy² is in class 42A.

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