Since the group $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{10} \rangle$ seems to have resisted attacks of some powerful programs, I will turn to a group that seems to be a bit easier to analyse. The group

$H := \langle a, b, c \ | \ a^2, b^2, c^2, (ab)^2, (ac)^3, (bc)^7, (abc)^{19} \rangle$

only has one of the simple groups that are a quotient of G, J1. Therefore it seems it will be easier to analyse. Adding the relation (abcbc)^i give the trivial group for all i less than 25 except for 15, where it gives J1. What is the group

$I := \langle a, b, c \ | \ a^2, b^2, c^2, (ab)^2, (ac)^3, (bc)^7, (abc)^{19}, (abcbc)^{25} \rangle$?

I have checked on magma using knuth bendix, and it takes too long, so magma stops the calculation.