Solved with three auxiliary generators

3 unique, 14 total

Σ#PresentationPropertiesφ
Solved by morph:3/0,3/0,3/0:
82228⟨a, b, c | aabc=1, cbac=1⟩Grp Inf11
Solved by morph:2/1,2/2,2/1:
82794⟨a, b, c | abc=b, caaa=1⟩Noc Inf
Solved by morph:2/1,3/2,3/2:
87025⟨a, b, c | ab=1, bbbca=c⟩Noc Inf