Generators and Representations for G = S₄(5)

Standard generators

• Standard generators of S₄(5) are a and b where a is in class 2B, b is in class 3B and ab is in class 13C. The last condition is equivalent to: ab has order 13 and ababb has order 12. (Source: ATLAS)
• Standard generators of 2.S₄(5) are preimages A and B where B has order 3 and AB has order 13. (Source: ATLAS)

BBOX programs

• Checker for S₄(5)
• CCL rep tester for S₄(5)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
S4(5)	13	+	13(a)	χ2	C			75%		1.3	perm rep on 312b pts
			13(b)	χ3	C			75%		1.3	Galois conjugate of χ2
S4(5)	40	+	40	χ4	Z			85%	5	7.4	perm rep on 600 pts
S4(5)	65	+	65(a)	χ5	Z			91%	5	18.2	perm rep on 156b pts
			65(b)	χ6	Z			92%	4	18.1	perm rep on 156a pts
S4(5)	78	+	78(a)	χ7	C			90%		56.1	perm rep on 312a pts
			78(b)	χ8	C			90%		56.1	Galois conjugate of χ7
S4(5)	90	+	90	χ9	Z			91%	6	34.4	perm rep on 156b pts
S4(5)	104	+	104(a)	χ10	Z			68%	29	49.0	perm rep on 780a pts
			104(b)	χ11	Z			79%	31	47.7	perm rep on 300 pts, LLL'ed
			104(c)	χ12	Z			94%	3	45.7	perm rep on 600 pts
S4(5)	130	+	130	χ13	Z			97%	4	70.7	perm rep on 312b pts
S4(5)	156	+	156	χ14	Z			81%	69	106.3	perm rep on 600 pts, LLL'ed
S4(5)	208	+	416	χ15+χ16	Z			71%	14733	976.7	perm rep on 3250 pts
2.S4(5)	12	-	No representations available
2.S4(5)	52	-	No representations available
2.S4(5)	104	-	No representations available
2.S4(5)	156	-	No representations available
2.S4(5)	208	-	No representations available

Notes

(xy)⁵xy²xy²xyxy² is in class 30A.

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