Generators and Representations for G = L₂(23)

Standard generators

• Standard generators of L2(23) are a and b where a has order 2, b has order 3 and ab has order 23. (Source: ATLAS)
• Standard generators of the double cover 2.L2(23) = SL2(23) are pre-images A and B where B has order 3 and AB has order 23. (Source: ATLAS)

BBOX programs

• Finder for L₂(23)
• Checker for L₂(23)
• CCL rep tester for L₂(23)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L2(23)	11	o	11(a)	χ2	C			72%		12.7	Weil rep - reseeded
			11(b)	χ3	C			72%		12.6	Weil rep - reseeded
L2(23)	22	+	22(a)	χ4	Z			76%	6	2.7	perm rep on 506 pts (cosets of D12 = 2 x S3)
			22(b)	χ5	Z			69%	7	2.7	perm rep on 253 pts (cosets of S4)
			22(c)	χ6	Z			80%	4	2.6	perm rep on 253 pts (cosets of S4)
			22(d)	χ7	C			80%		15.5	perm rep on 253 pts (cosets of S4)
			22(e)	χ8	C			80%		15.5	perm rep on 253 pts (cosets of S4)
L2(23)	23	+	23	χ9	Z			91%	1	2.8	perm rep on 24 pts
L2(23)	24	+	24(a)	χ10	C			95%		3.1	induce from Borel
			24(b)	χ11	C			95%		3.1	induce from Borel
			24(c)	χ12	C			95%		3.1	induce from Borel
			24(d)	χ13	C			95%		3.1	induce from Borel
			24(e)	χ14	C			95%		3.1	induce from Borel
2.L2(23)	12	o	No representations available
2.L2(23)	22	-	No representations available
2.L2(23)	24	-	No representations available

Notes

Identifying classes: 11D is abababb, 12B is ababb

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