On Thompson’s Conjecture for Alternating Groups 𝐴_𝑝+3

Table 2

The simple exceptional group.

𝐿	𝐋	𝑑	𝑂	|𝐿|
𝐺2(𝑞)	2	1	𝑓, if 𝑝≠3	𝑞^6𝑞^2−1𝑞^6−1
			2𝑓, if 𝑝=3
𝐹4(𝑞)	4	1	(2,𝑝)𝑓	𝑞^24𝑞^2−1𝑞^6−1𝑞^8−1𝑞^12−1
𝐸6(𝑞)	6	(3,𝑞−1)	2𝑑𝑓	1𝑑𝑞^36∏𝑖∈{2,5,6,8,9,12}𝑞^𝑖−1
𝐸7(𝑞)	7	(2,𝑞−1)	𝑑𝑓	1𝑑𝑞^63∏𝑖∈{2,6,8,10,12,14,18}𝑞^𝑖−1
𝐸8(𝑞)	8	1	𝑓	𝑞^120∏𝑖∈{2,8,12,14,18,20,24,30}𝑞^𝑖−1
^2𝐵2(𝑞),𝑞=2^2𝑚+1	1	1	𝑓	𝑞^2𝑞^2+1𝑞−1
^2𝐺2(𝑞),𝑞=3^2𝑚+1	1	1	𝑓	𝑞^3𝑞^3+1𝑞−1
^2𝐹4(𝑞),𝑞=2^2𝑚+1	2	1	𝑓	𝑞^12𝑞^6+1𝑞^4−1𝑞^3+1𝑞−1
^3𝐷4(𝑞)	2	1	3𝑓	𝑞^12𝑞^8+𝑞^4+1𝑞^6−1𝑞^2−1
^2𝐸6(𝑞)	4	(3,𝑞+1)	2𝑑𝑓	1𝑑𝑞^36∏{}𝑖∈2,5,6,8,9,12𝑞^𝑖−(−1)^𝑖