I have a graph (as shown in figure), which represents a quotient of the group $$G=\langle A,B,C,D; A^3=B^2=C^3=D^2=(AC)^2=(AD)^2=(BC)^2=(BD)^2=1 \rangle.$$ I proved that $G$ acts 2-transitively and so primitively. I happen to know the permutation group of this graph is alternating group Alt(17), but how can I show theoretically that this graph represents Alt(17)?
