Generators and Representations for G = McL

Standard generators

• Standard generators of the McLaughlin group McL are a and b where a is in class 2A, b is in class 5A, ab has order 11 and ababababbababbabb has order 7. (Source: ATLAS)
• Standard generators of the triple cover 3.McL are preimages A and B where A has order 2 and B has order 5. (Source: ATLAS)
• Standard generators of the automorphism group McL:2 are c and d where c is in class 2B, d is in class 3B, cd has order 22 and cdcdcdcddcdcddcdd has order 24. (Source: ATLAS)

BBOX programs

• Finder for McL
• Finder for McL.2
• Checker for McL
• Checker for McL.2
• CCL rep tester for McL

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
McL	22	+	22	χ2	Z			87%	1	2.5	perm rep on 275 pts
McL	231	+	231	χ3	Z			97%	2	221.0	exterior square of 22-dim
3.McL	126	o	No representations available

Last generated on Sat Sep 24 18:52:43 2005