Generators and Representations for G = L₂(25)

Standard generators

• Standard generators of L₂(25) are a and b where a has order 2, b has order 3, ab has order 13 and ababb has order 4. These conditions ensure that ab is in class 13A/B. (Source: ATLAS)
• Standard generators of the double cover 2.L₂(25) = SL₂(25) are pre-images A and B where B has order 3 and AB has order 13. (Source: ATLAS)

BBOX programs

• Finder for L₂(25)
• Checker for L₂(25)
• CCL rep tester for L₂(25)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L2(25)	13	+	13(a)	χ2	Z			81%	2	1.3	perm rep on 65a pts
			13(b)	χ3	Z			82%	2	1.3	perm rep on 65b pts
L2(25)	24	+	144	χ4+χ5+χ6+χ7+χ8+χ9	Z			77%	49	92.1	perm rep on 300 pts
L2(25)	25	+	25	χ10	Z			94%	1	3.1	perm rep on 26 pts
L2(25)	26	+	26(a)	χ11	Z(ω)			96%		3.3	induce from Borel
			26(b)	χ12	Z(i)			96%		3.3	induce from Borel
			26(c)	χ13	Z(ω)			96%		3.3	induce from Borel (corrected)
			26(d)	χ14	C			96%		3.3	Borel (corrected)
			26(e)	χ15	C			96%		3.3	Borel (corrected)
2.L2(25)	12	-	No representations available
2.L2(25)	24	-	No representations available
2.L2(25)	26	-	No representations available

Notes

We assume that abbabbabababab is in class 12A rather than 12B. We further assume that abb(abbabab)^2(ab)^2 is in class 5A rather than 5B

Last generated on Sat Sep 24 18:52:58 2005