Generators and Representations for G = J₂

Standard generators

• Standard generators of the Janko group J₂ are a and b where a is in class 2B, b is in class 3B, ab has order 7 and ababb has order 12. (Source: ATLAS)
• Standard generators of the double cover 2.J₂ are preimages A and B where B has order 3, and AB has order 7. (Source: ATLAS)
• Standard generators of the automorphism group J₂:2 are c and d where c is in class 2C, d is in class 5AB and cd has order 14. (Source: ATLAS)

BBOX programs

• Finder for J₂
• Finder for J₂.2
• Checker for J₂
• Checker for J₂.2
• CCL rep tester for J₂

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
J2	14	+	14(a)	χ2	C			73%		2.6	perm rep on 315 pts
			14(b)	χ3	C			73%		2.6	perm rep on 315 pts
			28	χ2+χ3	Z			88%	4	3.7	perm rep on 315 pts
J2	21	+	21(a)	χ4	C			83%		4.3	perm rep on 560 pts
			21(b)	χ5	C			83%		4.2	perm rep on 560 pts
			42	χ4+χ5	Z			90%	7	8.0	perm rep on 560 pts
J2	36	+	36	χ6	Z			94%	1	5.9	perm rep on 100 pts
J2	63	+	63	χ7	Z			96%	2	16.8	perm rep on 100 pts
J2	70	+	140	χ8+χ9	Z			95%	5	82.0	perm rep on 1050 pts
J2	90	+	90	χ10	Z			74%	12	35.7	perm rep on 280 pts
J2	126	+	126	χ11	Z			95%	6	66.0	perm rep on 280 pts
J2	160	+	160	χ12	Z			91%	19	107.2	perm rep on 315 pts
J2	175	+	175	χ13	Z			96%	39	127.6	perm rep on 525 pts
J2	189	+	378	χ14+χ15	Z			80%	452	668.0	perm rep on 2016 pts
J2	224	+	448	χ16+χ17	Z			86%	258	878.1	perm rep on 1575 pts
J2	225	+	225	χ18	Z			81%	141	222.8	perm rep on 840 pts
2.J2	6	-	No representations available
2.J2	14	-	No representations available
2.J2	50	o	No representations available
2.J2	56	-	No representations available
2.J2	64	-	No representations available
2.J2	84	-	No representations available
2.J2	126	-	No representations available
2.J2	216	-	No representations available

Last generated on Sat Sep 24 18:52:40 2005