Original sentence: The quaternion group Q may be regarded as acting on the  eight nonzero elements of the 2-dimensional vector space over the finite field GF(3)
Edited sentence: Indeed, the group SL(2, 3) has order 24, and Q is a normal subgroup of SL(2, 3) of index 3.Since all of the above matrices have unit determinant over GF(3), this is a representation of Q in the special linear group SL(2, 3).The corresponding representation.There is also an important action of Q on the eight nonzero elements of the 2-dimensional vector space over the finite field GF(3).is given by.where {−1,0,1} are the three elements of GF(3)