My conjecture is that the groups (a,b|a^2, b^3, (ab)^7, [a,b]^9, (([a,b]^4)b)^2p)) have a composition series: PSL(2,8)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p)-Z(p). Is there any literature on this subject, and if not, how do I prove the conjecture?