Generators and Representations for G = M₁₂

Standard generators

• Standard generators of M₁₂ are a and b where a is in class 2B, b is in class 3B and ab has order 11. (Source: ATLAS)
• Standard generators of the double cover 2.M₁₂ are preimages A and B where A is in class +2B, B has order 6 and AB has order 11. (Note that any two of these conditions imply the third.) (Source: ATLAS)
• Standard generators of M₁₂:2 are c and d where c is in class 2C, d is in class 3A and cd is in class 12A. (This last condition can be replaced by: cd has order 12 and cdcdd has order 11.) (Source: ATLAS)

BBOX programs

• Finder for M₁₂
• Finder for M₁₂.2
• Checker for M₁₂
• Checker for M₁₂.2
• CCL rep tester for M₁₂

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
M12	11	+	11(a)	χ2	Z			82%	1	1.0	perm rep on 12a pts
			11(b)	χ3	Z			82%	1	1.0	perm rep on 12a pts
M12	16	o	16(a)	χ4	C			67%		12.4	perm rep on 144 pts, vect exch
			16(b)	χ5	C			67%		12.4	complex conjugate of χ4
			32	χ4+χ5	Z			91%	1	4.7	perm rep on 144 pts
M12	45	+	45	χ6	Z			89%	25	9.0	perm rep on 144 pts, LLL
M12	54	+	54	χ7	Z			96%	1	12.5	perm rep on 132(2) pts
M12	55	+	55(a)	χ8	Z			93%	2	13.1	perm rep on 132(1) pts
			55(b)	χ9	Z			95%	3	13.0	χ10 with B->B^-1
			55(c)	χ10	Z			95%	3	13.0	perm rep on 440 pts
M12	66	+	66	χ11	Z			98%	1	18.6	perm rep on 132(2) pts
M12	99	+	99	χ12	Z			91%	11	41.7	perm rep on 220 pts, LLL'ed
M12	120	+	120	χ13	Z			80%	16	62.5	perm rep on 440 pts, vect exch by hand
M12	144	+	144	χ14	Z			83%	13	89.2	perm rep on 396 pts, vect exch by hand
M12	176	+	176	χ15	Z			71%	196	145.8	perm rep on 660 pts
2.M12	10	o	No representations available
2.M12	12	+	12	χ18	Z			91%	1	1.1	perm rep on 24 pts
2.M12	32	-	No representations available
2.M12	44	o	No representations available
2.M12	110	o	220	χ22+χ23	Z			99%	1	198.7	exterior cube of 12-dim rep
2.M12	120	+	120	χ24	Z			97%	2	59.8	perm rep on 288 pts
2.M12	160	o	No representations available

Last generated on Sat Sep 24 18:52:37 2005