Generators and Representations for G = L₂(29)

Standard generators

• Standard generators of L2(29) are a and b where a has order 2, b has order 3 and ab has order 29. (Source: ATLAS)
• Standard generators of the double cover 2.L2(29) = SL2(29) are pre-images A and B where B has order 3 and AB has order 29. (Source: ATLAS)

BBOX programs

• Finder for L₂(29)
• Checker for L₂(29)
• CCL rep tester for L₂(29)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L2(29)	15	+	15(a)	χ2	C			80%		22.3	perm rep on 60 pts
			15(b)	χ3	C			80%		22.3	perm rep on 60 pts
			30(g)	χ2+χ3	Z			96%	1	4.2	perm rep on 60 pts
L2(29)	28	+	28(a)	χ4	Z			88%	4	3.8	perm rep on 406 pts (cosets of D30)
			28(b)	χ5	C			85%		6.4	perm rep on 406 pts (cosets of D30)
			28(c)	χ6	C			85%		6.4	perm rep on 406 pts (cosets of D30)
			56	χ5+χ6	Z			83%	19	14.0	perm rep on 406 pts (cosets of D30)
			112	χ7+χ8+χ9+χ10	Z			67%	56	57.9	perm rep on 406 pts (cosets of D30)
L2(29)	29	+	29	χ11	Z			93%	1	4.1	perm rep on 30 pts: standard generators this time!
L2(29)	30	+	30(a)	χ12	C			96%		4.4	induce from Borel
			30(b)	χ13	C			96%		4.4	induce from Borel
			30(c)	χ14	C			96%		4.4	induce from Borel
			30(d)	χ15	C			96%		4.5	induce from Borel
			30(e)	χ16	C			96%		4.5	induce from Borel
			30(f)	χ17	C			96%		4.5	induce from Borel
2.L2(29)	14	-	No representations available
2.L2(29)	28	-	No representations available
2.L2(29)	30	-	No representations available

Notes

Identifying classes: 14A is ab(ababb)^2. 7B is its square. 15C is abababb.

Last generated on Sat Sep 24 18:52:59 2005