<Dl> <Dd> Q = ⟨ e _̄, i, j, k ∣ e _̄ 2 = e, i 2 = j 2 = k 2 = i j k = e _̄ ⟩, (\ displaystyle \ mathrm (Q) = \ langle (\ bar (e)), i, j, k \ mid (\ bar (e)) ^ (2) = e, \; i ^ (2) = j ^ (2) = k ^ (2) = ijk = (\ bar (e)) \ rangle,) </Dd> </Dl> <Dd> Q = ⟨ e _̄, i, j, k ∣ e _̄ 2 = e, i 2 = j 2 = k 2 = i j k = e _̄ ⟩, (\ displaystyle \ mathrm (Q) = \ langle (\ bar (e)), i, j, k \ mid (\ bar (e)) ^ (2) = e, \; i ^ (2) = j ^ (2) = k ^ (2) = ijk = (\ bar (e)) \ rangle,) </Dd> <P> where e is the identity element and e commutes with the other elements of the group . </P> <P> The Q group has the same order as the dihedral group DiH, but a different structure, as shown by their Cayley and cycle graphs: </P>

Order of sylow 2 subgroup of q8 is