The other class #92;mathcal#123;C#125;#95;2 of loops consists of 3-dimensional connected differentiable left A-loops such that the group G#61;PSL#95;2(#92;mathbbR)#92;ltimes#92;mathbbR³ is the group topologically generated by the left translations The loops in this class can be represented by two real parameters a,b and form precisely two isomorphism classes, which coincide with the isotopism classes.
Source: wiktionary